Question

Find the LCD of$\frac{5}{c^2-4c+4},\frac{3c}{c^2-10c+16}$.

Short answer

The LCD is$(c-2{)}^2(c-8)$.

Step-by-step solution

Given Information

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

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.

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

 Determine the common factors and from the remaining factors, multiply each of the denominator with appropriate factors.

The common factor is $(c-2)$.

Multiply common factor with other factors.

$=(c-2)(c-2)(c-8)$

$=(c-2{)}^2(c-8)$