Divide ((x+5)/(x-6))÷((x-2)/(x^2-x-30))

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -30}$ and whose sum is ${\displaystyle -1}$.

Write the factored form using these integers.

Cancel the common factor.

Rewrite the expression.

Raise ${\displaystyle x+5}$ to the power of ${\displaystyle 1}$.

Raise ${\displaystyle x+5}$ to the power of ${\displaystyle 1}$.

Use the power rule ${\displaystyle a^m{a}^n=a^{m+n}}$ to combine exponents.

Add ${\displaystyle 1}$ and ${\displaystyle 1}$.