ANSWER
[tex]3x-5[/tex] , [tex]x\ne -\frac{5}{3}[/tex]
EXPLANATION
We want to simplify
[tex] \frac{9 {x}^{2} - 25}{3x + 5} [/tex]
We rewrite the numerator as difference of two squares.
[tex]\frac{(3 {x})^{2} - {5}^{2} }{3x + 5} [/tex]
Factor the numerator using difference of two squares.
[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]
This implies that:
[tex]\frac{(3 {x})^{2} - {5}^{2} }{3x + 5} = \frac{(3 {x} + 5) (3x - 5)}{3x + 5}[/tex]
We cancel the common factors to get,
[tex] = 3x - 5[/tex]
For
[tex]x\ne -\frac{5}{3}[/tex]
