Simplify (x+5)/(2-x)(x^2-14x+33)/(x^2-13x+22)

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 ${\displaystyle 33}$ and whose sum is ${\displaystyle -14}$.

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 ${\displaystyle 22}$ and whose sum is ${\displaystyle -13}$.

Write the factored form using these integers.

Cancel the common factor.

Rewrite the expression.

Multiply ${\displaystyle \frac{x+5}{2-x}}$ and ${\displaystyle \frac{x-3}{x-2}}$.

Rewrite ${\displaystyle 2}$ as ${\displaystyle -1(-2)}$.

Factor ${\displaystyle -1}$ out of ${\displaystyle -x}$.

Factor ${\displaystyle -1}$ out of ${\displaystyle -1(-2)-\left(x\right)}$.

Reorder terms.

Raise ${\displaystyle x-2}$ to the power of ${\displaystyle 1}$.

Raise ${\displaystyle x-2}$ 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 ${\displaystyle 1}$.