Simplify ((5-x)/(x^2+3x-4))÷((x^2-2x-15)/(x^2+5x+4))

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 ${\displaystyle -4}$ and whose sum is ${\displaystyle 3}$.

Write the factored form using these integers.

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 ${\displaystyle 4}$ and whose sum is ${\displaystyle 5}$.

Write the factored form using these integers.

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 ${\displaystyle -15}$ and whose sum is ${\displaystyle -2}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle x+4}$.

Multiply ${\displaystyle \frac{5-x}{x-1}}$ by ${\displaystyle \frac{x+1}{(x-5)(x+3)}}$.

Cancel the common factor of ${\displaystyle 5-x}$ and ${\displaystyle x-5}$.

Move the negative in front of the fraction.