Class 7 Mathematics Exercise 6.1 Full solution

(1) Solution:- a² b/a³ c

= b/ac

(2) Solution:- a² b c/ab² c

= a/b

(3) Solution:- x³y³z³/x²y²z²

= x y z

(4) Solution:- x²+x/x y +y

= x(x+1)/y(x+1)

= X/y

(5) Solution:- 4a² b/6a³ b

= 4/6x a² b/a³ b

= 2/3×1/a

= 2/3a

(6) Solution:- 2a-4ab/1-4b²

= 2a (1-2b)/(1)²– (2b)²

= 2a (1-2b)/(1+2b) (1-2b)

= 2a/(1+2b)

(7) Solution:- 2a+3b/4a²-9b²

= 2a+3b/(2a)² – (3b)²

= 2a+3b/(2a+3b) (2a-3b)

= 1/2a-3b

(8) Solution:- a²+4a+4

= a²+2a+2a+4/(a)² – (2)²

= a(a+2)+2 (a+2)/(a+2) (a-2)

= (a+2) (a+2)/(a+2) (a-2)

= (a+2)/(a-2)

(9) Solution:- x2-y2/(x +y)2

= (x +y) (x-y)/ (x +y) (x +y)

= X-y/x +y

(10) Solution:- x²+2x-15/x² +9x+20

= x²+5x-3×15/x²+5x+4x+20

= X(x+5) -3 (x+5)/x (x-5) +4 (x+5)

= (x+5) (x-3)/(x+5) (x+4)

(11) Solution:- a/b c, d/a c

Denominator b c 8 ac, L.C.M= a b c

Therefore, a/ac = a x a/b c x a

= a²/a b c

And a/ac = a x b/a c x b

= a b/a b c

(12) Solution:- x/p q, y/p r

L.C.M of denominator = p q r

Therefore, x/p q = x X r/p q x r = x r/p q r

y/p r= y X x/p r x q = y q/p q r

(13) Solution:- 2x/3m, 3y/2n

L.C.M of denominator= 6mn

Therefore, 2x/3m = 2xX2n/3mx2n= 4xn/6n

= 3y/2n = 3yx3m/2mx3m= 9my/6mn

(14) Solution:- a/a-b, b/a +b

Therefore, L.C.M of denominator (a +b) (a-b)

Therefore, a/a-b= a x(a +b)/(a-b) (a +b) = a(a +b)/a² – b²

=> b /a +b = b x(a-b)/(a +b) (a-b) = b(a-b)/a² – b²

(15) Solution:- x²/a²-2ab, y²/a+2b

Therefore, L.C.M of denominator= (a+2b) (a²-2ab)

= (a+2b) (a-2b)a

Therefore, x²/a²-2ab= x²X(a²+2ab)/(a²-2ab) (a²+2ab)= x² (a²+2ab)/a (a²-4b²)

=> y²/a+2b= y²xa (a-2b)/(a+2b) (a-2b)a = ay² (a-2b)/a (a²-4b²)

(16) Solution:- 3/a²-4, 2/a (a+2)

L.C.M, of denomination, = (a²-4) a (a+2)

= a (a+2) (a-2)

3/a²-4 = 3xa/(a+2) (a-2)a

= 3a/a(a2-4)

2/a(a+2) = 2(a-2)/a(a+2) (a-2)

= 2 (a-2)/a(a²-4)

(17) Solution:- a/a²-9, b/a+3

Therefore, a²-9, (a)² – (3)² = (a+3) (a-3)

L.C.M of denominator= a (a+3) (a-3)

a/a²-9 = a. 1/(a+3) (a-3) = a/a² – 9

= b/(a+3) = b(a-3)/(a+3) (a-3) = b(a-3)/a² -9

(19) Solution:- a/a-b, b/a +b, c/a(a +b)

L.C.M, of denominator = a (a +b) (a-b)

a/ a-b = a x a(a +b) /(a-b) a(a +b)= a²(a +b)/a(a²-b²)

b /a +b= b x a (a-b)/(a +b) x a (a-b) = a b(a-b)/a (a²-b²)

c/a (a +b) = c x(a-b)/a (a +b) (a-b) = c(a-b)/a (a²-b²)

(20) Solution:- 2/x²– x- 2, 3/x²+x-6

= x²-x-2 = (x+1) (x-2)

X²+x-6= (x-3) (x-2)

Therefore, (x+1) (x-2) (x+3)

Therefore, 2/x²-x-2= 2x(x+3)/(x+1) (x-2) x (x+3)

3/x²+x-6 = 3x(x+1)/(x+3) (x-2) (x-1)