Chapter 6.6, Problem 11OE

To determine

Simplify: the given expression as fraction.

Answer to Problem 11OE

The simplified form of $\frac{5}{x-1}-2$ is $\frac{7-2x}{x-1}$.

Explanation of Solution

Given information:

The expression $\frac{5}{x-1}-2$.

Formula used:

Least common denominator: It is the smallest multiple of denominator of set of fractions.

  $\frac{5}{x-1}-2$

Recall that Least common denominator is the smallest multiple of denominator of set of fractions.

  $=\frac{5}{x-1}-\frac{2}{1}$

Least common denominator for $\frac{5}{x-1},\frac{2}{1}$ is $x-1$ . So,

  $\begin{array}{l}=\frac{5-2\left(x-1\right)}{x-1}\\ =\frac{5-2x+2}{x-1}\\ =\boxed{\frac{7-2x}{x-1}}\end{array}$

The simplified form of $\frac{5}{x-1}-2$ is $\frac{7-2x}{x-1}$.