Simplify: 18q2−45q+25/9q2−25.

Question

asked Jan 1, 2022 197k views

1 Answer

Ignatius Reilly · Answer 1 · 2022-01-07T21:08:37+0000

Answer:

((6q-5))/((3q+5))

Explanation:

Given:
(18q^(2)-45q+25 )/(9q^(2)-25 )

Factorizing the numerator and the denominator, we have:

18
q^(2) - 45q + 25 = 18
q^(2) - 30q - 15q + 25

= (3q - 5)(6q - 5)

and

9
q^(2) - 25 = (3q - 5)(3q + 5)

So that,

(18q^(2)-45q+25 )/(9q^(2)-25 ) =
((3q-5)(6q-5))/((3q-5)(3q+5))

=
((6q-5))/((3q+5))

Therefore,

(18q^(2)-45q+25 )/(9q^(2)-25 ) =
((6q-5))/((3q+5))