We are given the following expression:
[tex]\frac{v^3+125}{v^2-25}[/tex]To simplify the expression we will factor the numerator and denominator. To factor the numerator we will use the following:
[tex](a^3+b^3)=(a+b)(a^2-ab+b^2)[/tex]Applying the formula we get:
[tex]\frac{v^{3}+125}{v^{2}-25}=\frac{(v+5)(v^2-5v+25)}{v^2-25}[/tex]Now, we will factor the denominator using the following:
[tex](a^2-b^2)=(a+b)(a-b)[/tex]Applying the rule we get:
[tex]\frac{(v+5)(v^2-5v+25)}{v^2-25}=\frac{(v+5)(v^2-5v+25)}{(v+5)(v-5)}[/tex]Now, we can cancel out the "v + 5", and we get:
[tex]\frac{(v+5)(v^2-5v+25)}{(v+5)(v-5)}=\frac{v^2-5v+25}{v-5}[/tex]and thus we get the simplified form of the expression.
