NCERT Solutions for Chapter 14 Factorisation Class 8 Maths

Answer

(i) 12x = 2 × 2 × 3 × x 

36 = 2 × 2 × 3 × 3

Hence, the common factors are 2, 2 and 3 = 2 × 2 × 3 = 12

(ii) 2y = 2 ×y 

22xy = 2 ×11 × x ×y

Hence, the common factors are 2 and y = 2 × y = 2y 

(iii) 14pq = 2 × 7 × p × q

28p2q2 = 2 × 2 × 7 × p × p × q × q

Hence, the common factors are 2 × 7 × p × q = 14pq 

(iv) 2x = 2 × x × 1 

3x2 = 3 × x × x × 1

4= 2 × 2 ×1

Hence, the common factor is 1.

(v) 6abc = 2 ×3 ×a × b × c 

24ab2 = 2 × 2 × 2 ×3 × a × b × b

12a2b = 2 × 2 ×3 ×a × a × b 

Hence, the common factors are 2 ×3 × a ×b = 6ab 

(vi) 16x3 = 2 × 2 × 2 × x × x × x  

-4x2 = (-1) ×2 ×2 × x × x

32x = 2 × 2 × 2 × 2 × 2 × x 

Hence the common factors are 2 ×2 × x = 4x 

(vii) 10pq = 2 ×5 × p ×q 

20qr = 2 × 2 ×5 ×q × r

30rp = 2 × 3 ×5 ×r ×p

Hence the common factors are 2 × 5 = 10

(viii) 3x2y3 = 3 × x × x ×y ×y ×y 

10x3y2= 2 × 5 ×x × x ×x ×y ×y

6x2y2z = 2 ×3 × x × x × y × y × z  

Hence the common factors are x × x ×y ×y = x2y2 

Answer

(i) 7x - 42 = 7 × x - 2 ×3 ×7

Taking common factors from each term,

= 7(x - 2 × 3) 

= 7(x - 6) 

(ii) 6p - 12q = 2 × 3 ×p - 2 × 2 ×3 × q   

Taking common factors from each term,

= 2 × 3(p - 2q) 

= 6(p - 2q) 

(iii) 7a2 + 14a = 7 × a × a + 2 × 7 × a  

Taking common factors from each term,

= 7 × a (a + 2) 

= 7a(a + 2) 

(iv) -16z + 20z3

= (-1) × 2 × 2 × 2 × 2 × z + 2 ×2 ×5 ×z × z × z
Taking common factors from each term,

= 2 × 2 × z (-2 ×2 + 5 × z ×z) 

= 4z (-4 + 5z2)

(v) 20l2m + 30alm

= 2 ×2 ×5 × l × l ×m + 2 × 3 × 5 × a × l × m

Taking common factors from each term,

= 2 × 5 × l × m(2 ×l + 3 ×a)  

= 10lm(2l +3a) 

(vi) 5x2y - 15xy2 = 5 ×x ×x ×y + 3 × 5 × x ×y × y change the image with image_3310_1

Taking common factors from each term,

= 5 × x ×y (x - 3y) 

= 5xy(x - 3y) 

(vii)
10a2 - 15b2 + 20c2 

= 2 × 5 × a × a - 3 × 5 × b × b + 2 × 2 × 5 × c × c

Taking common factors from each term,

= 5(2 ×a × a - 3 ×b ×b + 2 × 2 × c × c) 

= 5(2a2 - 3b2 + 4c2) 

(viii) -4a2 + 4ab - 4ca

= (-1) × 2 ×2 ×a ×a + 2 × 2 ×a × b - 2 × 2 × c × a
Taking common factors from each term,

= 2 × 2 × a(-a + b -c) 

= 4a (-a + b - c)

(ix) x2yz + xy2z + xyz2

= x × x × y ×z + x × y × y × z + z ×y × z × z
Taking common factors from each term,

= x × y × z( x + y + z) 

= xyz(x + y +z)  

(x) ax2y + bxy2 + cxyz

= a × x × x × y + b × x × y × y + c × x × y × z
Taking common factors from each term,

= x × y(a × x + b × y + c × z) 

= xy(ax + by +cz) 

Answer

(i) x2 + xy + 8x + 8y = x(x + y) + 8(x + y) 

= (x + y)(x + 8) 

(ii) 15xy - 6x + 5y - 2 = 3x(5y - 2) + 1(5y - 2) 

= (5y -2)(3x + 1) 

(iii) ax + bx - ay - by = (ax + bx) - (ay + by) = x(a + b) - y(a + b) 

= (a + b)(x - y)

(iv) 15pq + 15 + 9q + 25p = 15pq + 25p + 9q + 15 

= 5p(3q + 5) + 3(3q + 5) 

= (3q + 5)(5p + 3) 

(v) z -7 + 7xy - xyz = 7xy - 7 - xyz + z 

= 7(xy - 1) - z(xy - 1) 

= (xy -1)(7 - z) = (-1)(1 - xy)(-1)(z - 7) 

= ( 1 - xy)( z - 7)

Answer

(i) a2 + 8a + 16 = a2 + (4 + 4)a + 4 × 4 

Using identity x2 + (a + b)x + ab = (x + a)(x + b), 

Here x = a, a = 4 and b = 4

a2 + 8a + 16 = (a + 4)(a + 4) = (a + 4)2

(ii) p2 - 10p + 25 = p2 +(-5-5)p + (-5)(-5) 

Using identity x2 + (a +b)x + ab = ( x + a)(x + b), 

Here x = p, a = -5 and b = -5 

p2 - 10p + 25 = (p -5)(p- 5) = (p - 5)2  

(iii) 25m2 + 30m + 9 = (5m)2 + 2 × 5m × 3 + (3)2 

  Using identity a2 + 2ab + b2 = (a + b)2 , here  a= 5m, b = 3

 25m2 + 30m + 9 = (5m + 3)2 

(iv) 49y2 + 84yz + 36z2 = (7y)2 + 2 × 7y × 6z + (6z)2 

Using identity a2 + 2ab + b2 = (a + b)2 , here a = 7y, b = 6z 

49y2 + 84yz + 36z2 = (7y + 6z)2

(v)  4x2 - 8x + 4 = (2x)2 - 2 × 2x ×2 + (2)2 

  Using identity a2 - 2ab + b2 = (a - b)2 , here a = 2x, b = 2

4x2 - 8x + 4 = (2x - 2)2

= (2)2 (x - 1)2 = 4( x - 1)2

(vi) 121b2 - 88bc + 16c2 = (11b)2 - 2 × 11b × 4c + (4c)2

  Using identity  a2 - 2ab + b2 = (a - b)2 , here a = 11b, b = 4c 

121b2 - 88bc + 16c2 = (11b - 4c)2  

(vii) (l + m)2 - 4lm 

= l2 + 2 × l ×m + m2 - 4lm [ ∵ (a + b)2 = a2 + 2ab + b2 ] 

= l2 + 2lm + m2 - 4lm 

= l2 - 2lm + m2 

= (l - m)2   [ ∵ (a- b)2 = a2 - 2ab + b2 ]

(viii) a4 + 2a2b2 + b4 = (a2)2 + 2 × a2 × b2 + (b2)2 

= (a2 + b2)2 [∵ (a + b)2 = a2 + 2ab + b ]  

Answer

(i) 4p2 - 9q2 = (2p)2 - (3q)2

= (2p -3q)(2p + 3q) [ ∵  a2 -  b2 = (a - b)(a +b)] 

(ii) 63a2 - 112b2 = 7(9a2 - 16b2) 

= 7 [ (3a)2 - (4b)2]

= 7(3a - 4b)(3a + 4b)  [ ∵  a2 -  b2 = (a - b)(a +b)] 

(iii) 49x2 - 36 = (7x)2 - (6)2

= (7x - 6)(7x + 6)   [ ∵  a2 -  b2 = (a - b)(a +b)] 

(iv) 16x5 - 144x3 = 16x3(x2 - 9) 

= 16x3 [(x)2 - (3)2]    

= 16x3 (x - 3)(x + 3)   [ ∵  a2 -  b2 = (a - b)(a +b)] 

(v) (l + m)2 - (l - m)2 

= [(l + m) + ( l - m)][(l + m)- (l - m)] [ ∵  a2 -  b2 = (a - b)(a +b)] 

= (l + m + l - m)(l + m - l +m) 

= (2l) (2m) = 4lm

(vi) 9x2y2 - 16 = (3xy)2 - (4)2

= (3xy - 4)(3xy + 4)   [ ∵  a2 -  b2 = (a - b)(a +b)] 

(vii) ( x2 - 2xy + y2) - z2 = ( x - y)2 - z2  [ ∵ (a -b)2 = a2 -2ab + b2]

 = ( x - y - z)( x - y + z)  [ ∵  a2 -  b2 = (a - b)(a +b)] 

(viii) 25a2 - 4b2 + 28bs - 49c2 

= 25a2 - (4b2 - 28bc + 49c2) 

= 25a2 - [ (2b)2 - 2 × 2b × 7c + (7c)2] 

= 25a2 - (2b - 7c)2   [ ∵ (a -b)2 = a2 -2ab + b2]

= (5a)2 - (2b - 7c)2 

= [5a - (2b - 7c)][5a + (2b - 7c)]   [ ∵  a2 -  b2 = (a - b)(a +b)] 

= (5a - 2b + 7c)(5a + 2b - 7c) 

Answer

(i) ax2 + bx = x(ax + b) 

(ii) 7p2 + 21q2 = 7(p2 + 3q2) 

(iii) 2x3 + 2xy2 + 2xz2 = 2x( x2 + y2 + z2) 

(iv) am2 + bm2 + bn2 + an2 

= m2( a + b) + n2(a + b)

= (a + b )(m2 + n2) 

(v) (lm + l) + m + 1 = l(m + 1) + 1(m + 1) 

= (m + 1)( l + 1) 

(vi) y(y + z) + 9(y + z) = (y + z)(y + 9) 

(vii) 5y2 - 20y - 8z + 2yz 

= 5y2 - 20y + 2yz - 8z 

= 5y(y - 4) + 2z(y - 4) 

= (y - 4)(5y + 2z) 

(viii) 10ab + 4a + 5b + 2 

= 2a(5b + 2) + 1 (5b + 2) 

= (5b + 2)(2a + 1) 

(ix) 6xy - 4y + 6 - 9x 

= 6xy - 9x - 4y + 6 

= 3x(2y - 3) - 2(2y - 3) 

= (2y - 3) (3x - 2) 

Answer

(i) a4 - b4 = (a2)2 - (b2)2 

= (a2 - b2)( a2 + b2)       [ ∵  a2 -  b2 = (a - b)(a +b)] 

= (a - b)(a + b)(a2 + b2)    [ ∵  a2 -  b2 = (a - b)(a +b)] 

(ii) p4 - 81 = (p2)2 - (9)2 

= (p2 - 9)(p2 + 9)    [ ∵  a2 -  b2 = (a - b)(a +b)] 

= (p2 - 32)(p2 + 9) 

= ( p - 3)(p + 3)(p2 + 9)   [ ∵  a2 -  b2 = (a - b)(a +b)] 

(iii) x4 - (y + z)4 = (x2)2 - [(y + z)2]2 

= [x2 - (y + z)2][ x2 + (y + z)2]  [ ∵  a2 -  b2 = (a - b)(a +b)] 

= [x -(y +z)][x + (y + z)][x2 + (y + z)2]  [ ∵  a2 -  b2 = (a - b)(a +b)] 

= (x - y - z) (x + y + z) [x2 + (y + z)2]

(iv) x4 - (x - z)4 = (x2)2 - [(x - z)2]2 

= [x2 -(x - z)2][x2 + (x - z)2]  [ ∵  a2 -  b2 = (a - b)(a +b)] 

= [x - (x - z)][x + (x - z)] [x2 + (x - z)2]  [ ∵  a2 -  b2 = (a - b)(a +b)] 

= [x - x + z] [x + x - z] [x2 + x2 - 2xz + z2]  [ ∵ (a -b)2 = a2 -2ab + b2]

= z (2x - z) (2x2 - 2xz + z2) 

(v) a4 - 2a2b2 + b4 = (a2)2 - 2a2b2 + (b2)2 

= (a2 - b2)2      [ ∵  a2 -  b2 = (a - b)(a +b)] 

= [(a - b)(a + b)]2   [ ∵  a2 -  b2 = (a - b)(a +b)] 

= (a -b)2 (a + b)2 [ (xy)m = xmym] 

Answer

(i) p2 + 6p + 8 = p2 + ( 4 + 2)p + 4 × 2 

= p2 + 4p + 2p + 4 ×2  

= p(p + 4) + 2 ( p + 4)

= (p + 4)(p + 2) 

(ii) q2 - 10q + 21 = q2 - ( 7 + 3)q + 7 × 3

= q2 - 7q - 3q + 7 × 3 

= q(q - 7) - 3(q - 7) 

= (q - 7)( q - 3) 

(iii) p2 + 6p - 16 = p2 + (8 - 2)p - 8 × 2 

= p2 + 8p - 2p - 8 × 2

= p(p + 8) - 2(p + 8) 

= ( p + 8)(p -2)

Answer

 (i) 2x4 ÷ 56x = 28x4/56x

= 28/56 × x4/x 

= 1/2 x3  [ xm ÷ xn = xm-n ] 

(ii) -36y3 ÷ 9y2 = -36y3/9y2 

= -36/9 × y3/y2 

= -4y    [ xm ÷ xn = xm-n ] 

(iii) 66pq2r3 ÷ 11qr2 

= 66pq2r3/11qr2 

= 66/11 × pq2r3/qr2 

= 6pqr    [ xm ÷ xn = xm-n ] 

(iv) 34x3y3z3 ÷ 51xy2z3 

= 34x3y3z3/51xy2z3

= 34/51 ×x3y3z3/xy2z3 

= 2/3x2y    [ xm ÷ xn = xm-n ] 

(v) 12a8b8 ÷ (- 6a6b4) 

= 12a8b8/- 6a6b4

= 12/-6 × a8b8/a6b4 

= -2a2b4      [ xm ÷ xn = xm-n ]

Answer

 (i) (5x2 - 6x) ÷3x 

= (5x2 - 6x)/3x

= 5x2/3x - 6x/3x = (5/3)x - 2 = 1/3 (5x - 6)

(ii) (3y8 - 4y6 + 5y4) ÷ y4  

= (3y8 - 4y6 + 5y4)/ y4

= 3y8/y4 - 4y6/y4 + 5y4/y4 = 3y4 - 4y2 + 5 

(iii) 8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2  

= {8(x3y2z2 + x2y3z2 + x2y2z3)}/4x2y2z2 

= 8x3y2z2/4x2y2z2  + 8x2y3z2/4x2y2z2  + 8x2y2z3/4x2y2z2  

= 2x + 2y + 2z 

= 2(x + y + z) 

(iv) (x3 + 2x2 + 3x) ÷ 2x 

= (x3 + 2x2 + 3x)/2x 

= x3/2x + 2x2/2x + 3x/2x = x2/2 + 2x/2 + 3/2 

= 1/2( x2 + 2x + 3) 

(v) (p3q6 - p6q3) ÷ p3q3 

= (p3q6 - p6q3)/p3q3

= p3q6/p3q3 - p6q3/p3q3 = q3 - p3 

Answer

(i) (10x - 25) ÷ 5 = (10x - 25)/5 

= {5(2x - 5)}/5 = 2x -5 

(ii) (10x - 25) ÷ (2x - 5) = (10x - 25)/(2x - 5) 

= {5(2x - 5)/(2x - 5) = 5 

(iii) 10y(6y + 21) ÷ 5(2y + 7) 

= {10y(6y + 21)}/5(2y + 7)

= {2 × 5 × y × 3(2y + 7)}/5(2y + 7) = 2 × y × 3 = 6y 

(iv) 9x2y2(3z - 24) ÷ 27xy(z - 8) 

= {9x2y2(3z - 24)}/27xy(z - 8)

= 9/27 × {xy × xy × 3(z - 8)}/xy(z - 8) = xy  

(v) 96abc(3a - 12)(5b - 30) ÷ 144(a- 4)(b - 6) 

= {96abc(3a - 12)(5b - 30)}/144(a - 4)(b - 6)

= {12 × 4 × 2 × abc × 3 (a-4) × 5(b-6)}/{12 × 4 × 3 (a - 4)(b - 6) 

= 10abc

Answer

(i) 5(2x + 1)(3x + 5) ÷ (2x + 1) 

= {5(2x + 1)(3x +5)}/(2x + 1)

= 5(3x + 5)

(ii) 26xy( x + 5)(y - 4) ÷ 13x(y - 4)

26xy( x + 5)(y -4) ÷ 13x(y - 4)

= {26xy(x + 5)(y - 4)}/13x(y - 4)

= {13 × 2 × xy(x + 5)(y - 4)}/13x(y - 4) = 2y(x + 5)

(iii) 52pqr( p + q)(q + r)( r + p) ÷ 104pq(q + r)(r + p)

= {52pqr(p + q)(q + r)( r + p)}/{52 × 2 × pq(q + r)(r + p)}

= (1/2)r (p + q)

(iv) 20( y + 4)(y2 + 5y + 3) ÷ 5(y + 4)

= {20(y + 4)(y2 + 5y + 3)}/5(y + 4)

= 4(y2 + 5y + 3)

(v) x( x + 1)(x + 2)(x + 3) ÷ x(x + 1)

= {x(x + 1)(x + 2)(x + 3)}/x(x + 1)

= (x + 2)(x + 3) 

Answer

(i) (y2 + 7y + 10) ÷ (y + 5) 

= (y2 + 7y + 10)/(y + 5) 

= {y2 + ( 2 + 5)y + 2 × 5}/(y +5) 

= (y2 + 2y + 5y + 2 × 5)/(y + 5) 

= {(y + 2)(y + 5)}/(y + 5)  [∵ x2 + (a+b)x + ab = (x +a)(x+b)]

= y + 2 

(ii) (m2 - 14m + 32) ÷ (m + 2) 

= (m2 - 14m + 32)/(m +2) 

= { m2 + (-16 + 2)m + (-16) × 2}/(m + 2) 

= {(m - 16)(m + 2)}/(m +2)  [∵ x2 + (a+b)x + ab = (x +a)(x+b)]

= (m - 16)

(iii) (5p2 - 25p + 20) ÷ (p -1) 

= (5p2 - 25p + 20)/(p -1)

= (5p2 - 20p -5p + 20)/(p -1) 

= {5p(p - 4) -5 (p - 4)}/(p -1) 

= {(5p - 5)(p - 4)}/(p -1) = {5(p -1)(p -4)}/(p - 1) 

= 5( p - 4) 

(iv) 4yz (z2 + 6z - 16) ÷ 2y(z + 8) 

= {4yz(z2 + 6z - 16)}/2y(z + 8)

= {4yz[z2 + (8 - 2)z + 8 × (-2)]}/2y(z + 8)

= {4yz(z - 2)(z + 8)}/2y(z + 8)   [∵ x2 + (a+b)x + ab = (x +a)(x+b)]

= 2z ( z -2) 

(v) 5pq(p2 - q2) ÷ 2p( p + q) 

= {5pq(p2 - q2)}/2p(p + q)

= {5pq(p - q)(p + q)}/2p( p + q) [ ∵ a2 - b2 = (a - b)(a + b)]  

= (5/2)q (p - q) 

(vi) 12xy(9x2 - 16y2) ÷ 4xy(3x + 4y) 

= {12xy (9x2 - 16y2)}/4xy(3x + 4y)

= {12xy[(3x)2 - (4y)2]}/4xy(3x + 4y)

= {12xy(3x - 4y)(3x + 4y)}/4xy(3x + 4y)   [ ∵ a2 - b2 = (a - b)(a + b)] 

= 3(3x - 4y) 

(vii) 39y3(50y2 - 98) ÷ 26y2(5y + 7)

= {39y3(50y2 - 98)}/26y2(5y + 7)

= {39y3 × 2(25y2 - 49)}/26y2(5y + 7)

= {39y2 × 2[(5y)2 - (7)2]}/26y2(5y + 7)

= {39y2 × 2(5y - 7)(5y + 7)}/26y2(5y + 7)    [ ∵ a2 - b2 = (a - b)(a + b)] 

= 3y(5y - 7)

Answer

L.H.S. = 4(x-5) = 4x- 20 ≠R.H.S.

Hence the correct mathematical statement is 4(x-5) = 4x- 20.

Answer

L.H.S. = x(3x+2) = 3x2+ 2 ≠ R.H.S.

Hence the correct mathematical statement is  x(3x+2) = 3x2+ 2

Answer

L.H.S. = 2x + 3y ≠ R.H.S.

Hence the correct mathematical statement is 2x+ 3y = 2x+ 3y

Answer

L.H.S. = x+ 2x + 3x = 6x ≠R.H.S.

Hence the correct mathematical statement is x+ 2x + 3x = 6x.

Answer

L.H.S. = 5y + 2y+ y - 7y = 8y-7y =y ≠ R.H.S.

Hence the correct mathematical statement is 5y+ 2y+y- 7y = 4

Answer

L.H.S. = 3x+ 2x = 5x ≠ R.H.S.

Hence the correct mathematical statement is 3x+ 2x = 5x

Answer

L.H.S. = (2x)2 + 4(2x) + 7 = 4x2 + 8x+ 7 ≠ R.H.S.

Hence the correct mathematical statement is  (2x)2 + 4(2x) + 7 = 4x2 + 8x+ 7

Answer

L.H.S. = (2x)2 + 5x = 4x2+ 5x ≠ R.H.S.

Hence the correct mathematical statement is  (2x)2 + 5x = 4x2+ 5x.

Answer

L.H.S. = (3x + 2)2 = 3x2 + 2 × 3x × 2+ (2)2 

= 9x2 + 12x + 4 ≠ RHS

Hence the correct mathematical statementsis (3x + 2)2 = 9x2 + 12X + 4 × 3x 

Answer

(a) L.H.S. = x2 + 5X + 4

Putting  x = -3 in given expression,

 = (-3)2 + 5(-3) + 4 = 9 - 15 + 4 = -2  R.H.S.

Hence x2 + 5X + 4  gives (-3)2 + 5(-3) + 4 = 9 - 15 + 4 = -2

(b) L.H.S. = x2 - 5X + 4 

Putting  x = -3 cin given expression,

 = (-3)2 - 5(-3) + 4 = 9 + 15 + 4 = 28  ≠ R.H.S.

Hence x2 - 5X + 4  gives (-3)2 - 5(-3) + 4 = 9 + 15 + 4 = 28

(c) L.H.S. = x2 + 5X 

Putting x= -3 in given expression,

 = (-3)2 + 5(-3) = 9 - 15 = -6 ≠ R.H.S.

Hence x2 + 5X  gives (-3)2 + 5(-3) = 9 - 15 = -6

Answer

 L.H.S. = (y-3)2 = y2 - 2 × y × 3 +(3)2  [ (a-b)2 = a2 - 2ab + b2]

= y2 - 6y + 9  ≠ R.H.S.

Hence the correct statement is  (y-3)2 = y2  -6y+ 9 

Answer

L.H.S. = (z+5)2 = z2 + 2 × z×5+ (5)2 

= z2 + 10z +25 [ (a-b)2 = a2 - 2ab + b2] 

Hence the correct statement is (z+5)2 = z2 + 10z + 25  

Answer

 L.H.S. =  (2a + 3b)(a-b) = 2a(a-b) + 3b(a-b) 

= 2a2 - 2ab + 3ab - 3b2 

= 2a2 + ab - 3b2  ≠ R.H.S.

Hence the correct statement is (2a +3b)(a-b) = 2a2 + ab - 3b2 

Answer

L.H.S. = (a+4)(a+2) =a(a+2) + 4(a+2) 

= a2 + 2a + 4a + 8 = a2 + 6a + 8 ≠ R.H.S.

Hence the correct statement is (a+4)(a+2) = a2+6a+ 8

Answer

L.H.S. = (a-4)(a-2) = a(a-2)-4(a-2)

 = a2 - 2a -4a+8 = a2- 6a + 8 ≠ R.H.S

Hence the correct statement is (a-4)(a-2) = a2- 6a + 8 

Answer

L.H.S. = 3x2/3x2 =1/1 = 1 ≠ R.H.S.

Hence the correct statement is 3x2/3x2 =1 

Answer

L.H.S. = 3x2 + 1 / 3x2 = 3x2/ 3x2 + 1/3x2   

= 1 + 1 / 3x2  R.H.S.

Hence the correct statement is 3x2 + 1 / 3x2 = 1 + 1 / 3x2  

Answer

L.H.S. = 3x/(3x+2) ≠ R.H.S.

Hence the correct statement is 3x/(3x+2) = 3x/(3x+2) 

Answer

L.H.S. = 3/(4x+3)  ≠ R.H.S.

Hence the correct statement is 3/(4x+3) = 3/(4x+3)  

Answer

L.H.S. = (4x+5)/4x = 4x/4x + 5/4x = 1 + 5/4x  ≠R.H.S.

Hence the correct statement is  (4x+ 5)/4x = 1 + 5/4x 

Answer

L.H.S. = (7x+5)/5 = 7x/5 + 5/5 = 7x/5 + 1 ≠ R.H.S.

Hence the correct statement is (7x+5)/5 = 7x/5 +1