Question

Write as equivalent rational expression with LCD$(c-2)(c-2)(c-8)$of$\frac{5}{c^2-4c+4},\frac{3c}{c^2-10c+16}$.

Short answer

The result is$\frac{5c-40}{(c-2)(c-2)(c-8)},\frac{3c^2-6c}{(c-2)(c-2)(c-8)}$.

Step-by-step solution

Given Information

The given expression is$\frac{5}{c^2-4c+4},\frac{3c}{c^2-10c+16}$.

The LCD is$(c-2)(c-2)(c-8)$.

Factor the denominator of both expressions.

The factored form of first denominator.

$c^2-4c+4=(c-2)(c-2)$

The factored form of second denominator.

$c^2-10c+16=(c-2)(c-8)$

The fractions in factored form is $\frac{5}{(c-2)(c-2)},\frac{3c}{(c-2)(c-8)}$.

Multiply each denominator by the 'missing' factor and multiplyeach numerator by the same factor.

$\frac{5(c-8)}{(c-2)(c-2)(c-8)},\frac{3c(c-2)}{(c-2)(c-2)(c-8)}$

Simplify the numerators.

Multiply the numerator using distributive property.

$\frac{5c-40}{(c-2)(c-2)(c-8)},\frac{3c^2-6c}{(c-2)(c-2)(c-8)}$.