Chapter 11.5, Problem 3AYU

To determine

The lowest form of the fraction $\frac{3x-12}{x^2-16}$.

Answer to Problem 3AYU

Solution:

The lowest form of the fraction $\frac{3x-12}{x^2-16}$ is $\frac{3}{\left(x+4\right)}$.

Explanation of Solution

Given information:

The given fraction $\frac{3x-12}{x^2-16}$.

Explanation:

To reduce the fraction in the lowest form, cancel out all common factors from the numerator and denominator.

Consider the fraction $\frac{3x-12}{x^2-16}$,

Here $3x-12$ is the numerator and $x^2-16$ is the denominator.

By factoring the numerator,

$3x-12=3\left(x-4\right)$

By factoring the denominator,

$x^2-16=\left(x-4\right)\left(x+4\right)$

Thus, the given fraction can be written in terms of these factors as below,

$\frac{3x-12}{x^2-16}=\frac{3\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}$ where, $x\ne 4$ and $x\ne -4$.

By cancelling the common factor,

$\frac{3x-12}{x^2-16}=\frac{3}{\left(x+4\right)}$

Thus, $\frac{3x-12}{x^2-16}=\frac{3}{\left(x+4\right)}$.

Therefore, the reduced lowest form of the fraction is $\frac{3}{\left(x+4\right)}$.