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

The answer to 1/(x-1)+x/(x+2)=2 is x=-1+sqrt(7),x=-1-sqrt(7)

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

The solution is x=-1+sqrt(7),x=-1-sqrt(7)

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

x = - 1 + 7, x = - 1 - 7

Decimal Notation

x = 1.64575 \dots, x = - 3.64575 \dots

Solution steps

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

Multiply by LCM

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

Solve

x + 2 + x (x - 1) = 2 (x - 1) (x + 2) : x = - 1 + 7, x = - 1 - 7

x = - 1 + 7, x = - 1 - 7

Verify Solutions

Find undefined (singularity) points:

x = 1, x = - 2

Combine undefined points with solutions:

x = - 1 + 7, x = - 1 - 7

0 = 1 - 2 x^{- 2}

\frac{3}{x - 4} = \frac{0.2}{- 8}

1 = \frac{2}{3} - \frac{x - 7}{x}

\frac{2 x - 1}{4 - 3 x} = \frac{3}{4}

x = \frac{- 20 x}{12 - 150 x}

What is the answer to 1/(x-1)+x/(x+2)=2 ?
The answer to 1/(x-1)+x/(x+2)=2 is x=-1+sqrt(7),x=-1-sqrt(7)
Solve for x: 1/(x-1)+x/(x+2)=2
The solution is x=-1+sqrt(7),x=-1-sqrt(7)