What is the answer to 1/(x-1)+x/(x+2)=4 ?

The answer to 1/(x-1)+x/(x+2)=4 is x=(-2+sqrt(34))/3 ,x=-(2+sqrt(34))/3

Solve for x: 1/(x-1)+x/(x+2)=4

The solution is x=(-2+sqrt(34))/3 ,x=-(2+sqrt(34))/3

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\frac{1}{x - 1} + \frac{x}{x + 2} = 4

x = \frac{- 2 + 34}{3}, x = - \frac{2 + 34}{3}

Decimal Notation

x = 1.27698 \dots, x = - 2.61031 \dots

Solution steps

\frac{1}{x - 1} + \frac{x}{x + 2} = 4

Multiply by LCM

x + 2 + x (x - 1) = 4 (x - 1) (x + 2)

Solve

x + 2 + x (x - 1) = 4 (x - 1) (x + 2) : x = \frac{- 2 + 34}{3}, x = - \frac{2 + 34}{3}

x = \frac{- 2 + 34}{3}, x = - \frac{2 + 34}{3}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = - 2

Combine undefined points with solutions:

x = \frac{- 2 + 34}{3}, x = - \frac{2 + 34}{3}

\frac{3}{x} = \frac{6}{5 x} + 1

\frac{1}{x} = 16 x

x = \frac{6 x - 8}{x}

\frac{t}{∣ t ∣} = 0

\frac{0.75}{2} = \frac{60}{x}

What is the answer to 1/(x-1)+x/(x+2)=4 ?
The answer to 1/(x-1)+x/(x+2)=4 is x=(-2+sqrt(34))/3 ,x=-(2+sqrt(34))/3
Solve for x: 1/(x-1)+x/(x+2)=4
The solution is x=(-2+sqrt(34))/3 ,x=-(2+sqrt(34))/3