Question

Write as equivalent rational expression with LCD$(y+7)(y+5)(y-6)$of$\frac{8}{y^2+12y+35},\frac{3y}{y^2+y-42}$.

Short answer

The result is$\frac{8y-48}{(y+7)(y+5)(y-6)},\frac{3y^2+15y}{(y+7)(y-6)(y+5)}$.

Step-by-step solution

Given Information

The given expression is$\frac{8}{y^2+12y+35},\frac{3y}{y^2+y-42}$.

The LCD is$(y+7)(y+5)(y-6)$.

Factor the denominator of both expressions.

The factored form of first denominator.

$y^2+12y+35=(y+7)(y+5)$

The factored form of second denominator.

$y^2+y-42=(y+7)(y-6)$.

The fractions in factored form is$\frac{8}{(y+7)(y+5)},\frac{3y}{(y+7)(y-6)}$.

 Compare with given LCD and multiply each denominator by the 'missing' factor and multiply each numerator by the same factor.

$\frac{8(y-6)}{(y+7)(y+5)(y-6)},\frac{3y(y+5)}{(y+7)(y-6)(y+5)}$

Simplify the numerators.

Multiply the numerator using distributive property.

$\frac{8y-48}{(y+7)(y+5)(y-6)},\frac{3y^2+15y}{(y+7)(y-6)(y+5)}$