Chapter 11.4, Problem 24P

Add or subtract, add/or simplify.

$\frac{m}{x}+\frac{4}{m\left(x-1\right)}$

To determine

To simplify the expression.

Answer to Problem 24P

The simplified expression is $\frac{m^{2}x-m^2+4x}{m{x}^2-mx}$ .

Explanation of Solution

Given information:

The given expression is:

  $\frac{m}{x}+\frac{4}{m\left(x-1\right)}$

Calculation :

The solution can be obtained by:

  $\begin{array}{l}\frac{m}{x}+\frac{4}{m\left(x-1\right)}\\ =\frac{\left(m\right)\left(mx-m\right)+\left(4\right)\left(x\right)}{\left(mx-m\right)\left(x\right)}\\ =\frac{m^{2}x-m^2+4x}{m{x}^2-mx}\end{array}$

Hence, the simplified expression is $\frac{m^{2}x-m^2+4x}{m{x}^2-mx}$ .