Simplify ((4-x)/(x^2+5x-6))÷((x^2-11x+28)/(x^2+7x+6))

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 ${\displaystyle -6}$ 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 ${\displaystyle 6}$ and whose sum is ${\displaystyle 7}$.

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 ${\displaystyle 28}$ and whose sum is ${\displaystyle -11}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle x+6}$.

Multiply ${\displaystyle \frac{4-x}{x-1}}$ by ${\displaystyle \frac{x+1}{(x-7)(x-4)}}$.

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

Move the negative in front of the fraction.