Verified answer

30)( 5a^2-45)/5a-15

=5(a^-9)/5(a-3)

=5{(a)^2-(3)^2}/5(a-3)

=5(a+3)(a-3)/5(a-3)

=a+3 [after eliminating 5(a-3)from both numerator and denominator]

32.y^2-2y)/(y^2-y-2)

=y(y-2)/(y-2)(y+1)

=y/(y+1)

34.(x^2+x-2)/(x^2+3x-4)

=(x+2)(x-1)/(x+4)(x-1)

=(x+2)/(x+4)

1.

(5a^2 - 45)/(5a - 15)

numerator = 5a^2 - 45

= 5(a^2 - 9)

=5(a + 3)(a -3) (since a^2 - b^2 = (a +b )a - b)

denominator = 5a - 15

=5(a - 3)

(5a^2 - 45)/(5a - 15) = 5(a + 3)(a - 3)/(5)(a - 3)

= (a + 3)

2.

(x^2 + x - 2)/(x^2 + 3x - 4)

numerator = x^2 + x - 2

=x^2 + 2x - x - 2

= x(x + 2) - 1(x + 2)

=(x - 1)(x + 2)

denominator = x^2 + 3x- 4

= x^2 + 4x - x - 4

=x(x + 4) - 1(x + 4)

=(x + 4) (x - 1)

(x^2 + x -2) /(x^2 + 3x - 4) = (x - 1)(x + 2)/(x + 4)(x - 1)

= (x + 2)/(x + 4)