Answer:
[tex]\frac{(6q-5)}{(3q+5)}[/tex]
Step-by-step explanation:
Given: [tex]\frac{18q^{2}-45q+25 }{9q^{2}-25 }[/tex]
Factorizing the numerator and the denominator, we have:
18[tex]q^{2}[/tex] - 45q + 25 = 18[tex]q^{2}[/tex] - 30q - 15q + 25
= (3q - 5)(6q - 5)
and
9[tex]q^{2}[/tex] - 25 = (3q - 5)(3q + 5)
So that,
[tex]\frac{18q^{2}-45q+25 }{9q^{2}-25 }[/tex] = [tex]\frac{(3q-5)(6q-5)}{(3q-5)(3q+5)}[/tex]
= [tex]\frac{(6q-5)}{(3q+5)}[/tex]
Therefore,
[tex]\frac{18q^{2}-45q+25 }{9q^{2}-25 }[/tex] = [tex]\frac{(6q-5)}{(3q+5)}[/tex]
