Evaluate 2/(x-2)+x/(x+9)-(x+20)/(x^2+7x-18)

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 ${\displaystyle -18}$ and whose sum is ${\displaystyle 7}$.

Write the factored form using these integers.

Multiply ${\displaystyle \frac{2}{x-2}}$ by ${\displaystyle \frac{x+9}{x+9}}$.

Multiply ${\displaystyle \frac{x}{x+9}}$ by ${\displaystyle \frac{x-2}{x-2}}$.

Reorder the factors of ${\displaystyle (x-2)(x+9)}$.

Combine the numerators over the common denominator.

Combine the numerators over the common denominator.

Simplify each term.

Simplify by adding terms.

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 ${\displaystyle -2}$ and whose sum is ${\displaystyle -1}$.

Write the factored form using these integers.

Cancel the common factor.

Rewrite the expression.