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

We have to solve the equation

`(5)/(x+8)=(3)/(x)`

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

`(5)/(x+8)-(3)/(x)=0`

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

Multiply both sides by LCM

`(5)/(x+8)x\left(x+8\right)-(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

`(5)/(12+8)=(3)/(12)`

`(5)/(20)=(1)/(4)`

`(1)/(4)=(1)/(4)`

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

A is the correct option.

Answer 2

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.