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. $\frac{5y-7}{20y+1}$
3. $\frac{x^{2}+2x-15}{x^{2}-2x-35}$

Explanation:

Step1: Factor numerator (Q7)

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

Step2: Factor denominator (Q7)

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

Step3: Cancel common factors (Q7)

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

Step4: Check for common factors (Q8)

$\frac{5y-7}{20y+1}$ has no shared factors

Step5: Factor numerator (Q9)

$x^2+2x-15=(x+5)(x-3)$

Step6: Factor denominator (Q9)

$x^2-2x-35=(x+5)(x-7)$

Step7: Cancel common factors (Q9)

$\frac{(x+5)(x-3)}{(x+5)(x-7)}=\frac{x-3}{x-7}, x
eq-5,7$

Answer:

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

eq-2,-7$)

1. Cannot be simplified
2. $\frac{x-3}{x-7}$ (where $x

eq-5,7$)