Question

multiplying and dividing rational expressions
rewrite the expression completely.
view solution history
$\frac{\frac{3y + 12}{(y + 3)(y + 4)}}{\frac{3}{2}}$
perform multiplication
$\frac{3y + 12}{(y + 3)(y + 4)} cdot \frac{2}{3}$
enter the result.

Explanation:

Step1: Factor numerator of first term

Factor out 3 from $3y+12$:
$3y+12 = 3(y+4)$

Step2: Rewrite the original expression

Substitute the factored form into the expression:
$\frac{3(y+4)}{(y+3)(y+4)} \cdot \frac{2}{3}$

Step3: Cancel common factors

Cancel $3$ and $(y+4)$ (where $y
eq -3, -4$):
$\frac{\cancel{3}\cancel{(y+4)}}{(y+3)\cancel{(y+4)}} \cdot \frac{2}{\cancel{3}}$

Step4: Simplify the remaining terms

Multiply the remaining parts:
$\frac{2}{y+3}$

Answer:

$\frac{2}{y+3}$ (where $y
eq -3, -4$)