Math

QuestionSolve for xx in the equation 1x+4=4x4\frac{1}{x+4}=\frac{4}{x-4}. What is xx?

Studdy Solution

STEP 1

Assumptions1. x is a real number. x ≠ -4 and x ≠4, because division by zero is undefined

STEP 2

The given equation is1x+4=4x4\frac{1}{x+4}=\frac{4}{x-4}To solve for x, we can start by cross multiplying.

STEP 3

Cross multiply the fractions(x+)=(x)1(x+) \cdot = (x-) \cdot1

STEP 4

implify the equation4x+16=x44x +16 = x -4

STEP 5

Subtract xx from both sides of the equation4xx=4164x - x = -4 -16

STEP 6

implify the equation3x=203x = -20

STEP 7

Finally, divide both sides by3 to solve for xxx=203x = \frac{-20}{3}So, the solution to the equation is x=203x = \frac{-20}{3}.

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