Question

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

1. $\frac{y^{2}+4y+4}{y^{2}+9y+14}$
2. $\frac{5y-7}{20y+1}$

Explanation:

Step1: Factor numerator

$y^2 + 4y + 4 = (y+2)^2$

Step2: Factor denominator

$y^2 + 9y + 14 = (y+2)(y+7)$

Step3: Cancel common factors

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

Step4: Check expression 8 for common factors

The numerator $5y-7$ and denominator $20y+1$ share no common factors (no common binomial or monomial divisors).

Answer:

1. $\frac{y+2}{y+7}$ (where $y

eq -2, -7$)

1. $\frac{5y-7}{20y+1}$ (cannot be simplified further)