Chapter A.3, Problem 60E

Solution

Simplify.

  $\frac{x+4}{x-2}$ .

Given:

The given fraction is $\frac{3}{x-2}+\frac{x+1}{x-2}$ .

Concept Used:

• Remove any grouping symbol such as brackets and parentheses by multiplying factors.
• Use the exponent rule to remove grouping if the terms are containing exponents.
• Combine the like terms by addition or subtraction.
• Combine the constants.

Calculation:

The given fraction is $\frac{3}{x-2}+\frac{x+1}{x-2}$ .

  $\begin{array}{c}\frac{3}{x-2}+\frac{x+1}{x-2}=\frac{3+x+1}{x-2}\\ =\frac{4+x}{x-2}\\ =\frac{x+4}{x-2}\end{array}$

Thus by simplifying $\frac{3}{x-2}+\frac{x+1}{x-2}$ to a single fraction it comes $\frac{x+4}{x-2}$ .