Question

simplify each rational expression. if the rational expression cannot be simplified, so state.

1. $\frac{y^{2}+4y+4}{y^{2}+9y+14}$

Explanation:

Step1: Factor numerator

Find two numbers that multiply to 4 and add to 4. These numbers are 2 and 2.
$y^2 + 4y + 4 = (y+2)^2$

Step2: Factor denominator

Find two numbers that multiply to 14 and add to 9. These numbers are 2 and 7.
$y^2 + 9y + 14 = (y+2)(y+7)$

Step3: Cancel common factors

Cancel the shared $(y+2)$ term from numerator and denominator (where $y
eq -2$).
$\frac{(y+2)^2}{(y+2)(y+7)} = \frac{y+2}{y+7}$

Answer:

$\frac{y+2}{y+7}$ (where $y
eq -2, -7$)