Question

Solve 5 over x plus 8 equals 3 over x for x, and determine if the solution is extraneous or not.

x = 12, non-extraneous
x = 12, extraneous
x = −12, non-extraneous
x = −12, extraneous

Answer 1

5 / (x+8) = 3/x
Cross-multiplying:
5x = 3(x + 8)
5x = 3x + 24
2x = 24
x = 12
Substituting x = 12 into the given:
5 / (12 + 8) = 3 / 12
1 / 4 = 1 / 4
No undefined values occurred, so x = 12 is non-extraneous, which is the first choice.

Answer 2

We have to solve the equation

$\frac{5}{x+8}=\frac{3}{x}$

In order to solve it for x, subtract 3/x to both sides

$\frac{5}{x+8}-\frac{3}{x}=0$

$\mathrm{Find\:Least\:Common\:Multiplier\:of\:}x+8,\:x:\quad x\left(x+8\right)$

Multiply both sides by LCM

$\frac{5}{x+8}x\left(x+8\right)-\frac{3}{x}x\left(x+8\right)=0\cdot \:x\left(x+8\right)$

On simplifying, we get

$5x-3x-24=0\\2x-24=0\\2x=24\\x=12$

To check the extraneous solution, we plugging this value of x in the given equation and check if it satisfies or not

$\frac{5}{12+8}=\frac{3}{12}$

$\frac{5}{20}=\frac{1}{4}$

$\frac{1}{4}=\frac{1}{4}$

This is true. Hence, x=12 is a solution (non-extraneous) to the given equation.

A is the correct option.