Simplify (y^2+11y+28)/(y^2+14y+49)

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.

Rewrite ${\displaystyle 49}$ as ${\displaystyle 7^2}$.

Check the middle term by multiplying ${\displaystyle 2ab}$ and compare this result with the middle term in the original expression.

Simplify.

Factor using the perfect square trinomial rule ${\displaystyle a^2+2ab+b^2={(a+b)}^2}$, where ${\displaystyle a=y}$ and ${\displaystyle b=7}$.

Factor ${\displaystyle y+7}$ out of ${\displaystyle (y+4)(y+7)}$.

Cancel the common factors.