Chapter A.5, Problem 46AYU

To determine

To find: LCM method of two rational expressions.

Answer to Problem 46AYU

$\frac{1}{4}+\frac{3}{x+1}=\frac{\left(x+1+3\right)}{4\left(x+1\right)}=\frac{x+4}{4\left(x+1\right)}$

Explanation of Solution

Given:

Two examples of adding two expressions.

Calculation:

Add two rational expressions $\frac{1}{4x}+\frac{3}{5x}$.

Then, $\frac{1}{4x}+\frac{3}{5x}=\frac{9x}{20x}=\frac{9}{20}$.

Another example:

Add two rational expressions $\frac{1}{4}+\frac{3}{x+1}$.

$\frac{1}{4}+\frac{3}{x+1}=\frac{\left(x+1+3\right)}{4\left(x+1\right)}=\frac{x+4}{4\left(x+1\right)}$