Simplify 3/(x+7)-(7x)/(x^2+9x+14)

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 ${\displaystyle 14}$ and whose sum is ${\displaystyle 9}$.

Write the factored form using these integers.

Multiply ${\displaystyle \frac{3}{x+7}}$ by ${\displaystyle \frac{x+2}{x+2}}$.

Reorder the factors of ${\displaystyle (x+7)(x+2)}$.

Apply the distributive property.

Multiply ${\displaystyle 3}$ by ${\displaystyle 2}$.

Subtract ${\displaystyle 7x}$ from ${\displaystyle 3x}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle -4x+6}$.

Factor ${\displaystyle -1}$ out of ${\displaystyle -2x}$.

Rewrite ${\displaystyle 3}$ as ${\displaystyle -1(-3)}$.

Factor ${\displaystyle -1}$ out of ${\displaystyle -\left(2x\right)-1(-3)}$.

Simplify the expression.