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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

User Rodfersou
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2 Answers

2 votes

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.

User Anthony Perez
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8.5k points
4 votes
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.
User Uriil
by
8.4k points

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