Chapter 7.5, Problem 31E

To determine

To describe: The error and correct the error in the first step of the solving the given equation.

Answer to Problem 31E

The LCD of $3x$ and $x$ is $3x^2$ . However, the student used $3x^3$ and also student forget to multiply $3x^2$ on both sides and only did it on the one side with the variable.

Explanation of Solution

Given:

The equation is $\frac{5}{3x}+\frac{2}{x^2}=1$ .

Calculation:

The LCD of $3x$ and $x$ is $3x^2$ . However, the student used $3x^3$ and also student forget to multiply $3x^2$ on both sides and only did it on the one side with the variable.

So, the correct step will be as follows.

  $\begin{array}{c}\frac{5}{3x}+\frac{2}{x^2}=1\\ 3x^2\cdot \frac{5}{3x}+3x^2\cdot \frac{2}{x^2}=1\left(3x^2\right)\end{array}$

Therefore, the LCD of $3x$ and $x$ is $3x^2$ . However, the student used $3x^3$ and also student forget to multiply $3x^2$ on both sides and only did it on the one side with the variable.