Chapter 11.8, Problem 1CYU

To determine

To solve: the each equation and state the extraneous solution.

Answer to Problem 1CYU

The value is $-2$ .

Since, $x=-2$ results in a zero in the denominator of the original equation, it is an extraneous solution.

Explanation of Solution

Given:

  $\frac{2}{x+1}=\frac{4}{x}$

Calculation:

The equation is solved below.

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

Conclusion:

Therefore, the value is $-2$ . Since, $x=-2$ results in a zero in the denominator of the original equation, it is an extraneous solution.