Simplifying Rational Expressions Using Factoring

Problem 215: Simplify

(1) $\begin{equation*} \frac{y^2 + 10y + 25}{y^2 + 11y + 30}. \end{equation*}$

Solution: In order to simplify the rational expression, we need to factor the numerator and denominator. That is,

Notice that the numerator and denominator are quadratic equation with leading coefficient 1. Thus

(2) $\begin{align*} \frac{y^2 + 10y + 25}{y^2 + 11y + 30} & = \frac{(y+5)(y+5)}{(y+6)(y+5)} \\ & = \frac{y+5}{y+6}\end{align*}$

That is,

(3) $\begin{equation*} \frac{y^2 + 10y + 25}{y^2 + 11y + 30} = \frac{y+5}{y+6}.\end{equation*}$

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