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QuestionSolve for xx: x+1x+34=−3x\frac{x+1}{x}+\frac{3}{4}=\frac{-3}{x}. What is xx?

Studdy Solution

STEP 1

Assumptions1. The equation is x+1x+34=−3x\frac{x+1}{x}+\frac{3}{4}=\frac{-3}{x} . We are solving for xx

STEP 2

First, we need to get rid of the fractions. We can do this by multiplying every term by 4x4x, which is the least common multiple of the denominators xx and 44.
4x⋅x+1x+4x⋅4=4x⋅−x4x \cdot \frac{x+1}{x} +4x \cdot \frac{}{4} =4x \cdot \frac{-}{x}

STEP 3

Now, simplify the equation by cancelling out the common factors.
(x+1)+3x=−12(x+1) +3x = -12

STEP 4

Expand the left side of the equation.
4x+4+3x=−124x +4 +3x = -12

STEP 5

Combine like terms on the left side of the equation.
7x+4=−127x +4 = -12

STEP 6

Subtract 44 from both sides of the equation to isolate the term with xx on the left side.
x=−12−4x = -12 -4

STEP 7

implify the right side of the equation.
7x=−167x = -16

STEP 8

Finally, divide both sides of the equation by 77 to solve for xx.
x=−167x = \frac{-16}{7}So, the solution to the equation is x=−167x = -\frac{16}{7}.

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