Question

Simplify: 18q2−45q+25/9q2−25.

Answer 1

`((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))`