Chapter A.6, Problem 1AYU

To determine

To find: The least common denominator of $\frac{3}{x^2-4}$ and $\frac{5}{x^2-3x+2}$.

Answer to Problem 1AYU

$\left(x+2\right)\left(x-2\right)\left(x-1\right)\\$

Explanation of Solution

Given:

$\frac{3}{x^2-4}$ and $\frac{5}{x^2-3x+2}$

Calculation:

Factor completely the polynomials in the denominator.

$x^2-4=\left(x+2\right)\left(x-2\right)$

$x^2-3x+2=(x-2)(x-1)$

Least common multiple of the denominator is $\left(x+2\right)\left(x-2\right)\left(x-1\right)\\$.