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

The answer to 2/(x-1)+x/(x-2)=1 is x= 3/2

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

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

x = \frac{3}{2}

Decimal

x = 1.5

Solution steps

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

Multiply by LCM

x^{2} + x - 4 = x^{2} - 3 x + 2

Move

4

to the right side

x^{2} + x = x^{2} - 3 x + 6

Subtract

x^{2} - 3 x

from both sides

x^{2} + x - (x^{2} - 3 x) = x^{2} - 3 x + 6 - (x^{2} - 3 x)

Simplify

4 x = 6

Divide both sides by

4

x = \frac{3}{2}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 2

Combine undefined points with solutions:

x = \frac{3}{2}

R, \frac{1}{R} = \frac{1}{r} + \frac{1}{s}

x^{- 1} + x = 3 x^{- 1}

\frac{4}{2 y - 3} = \frac{7}{3 y - 5}

34 - \frac{1}{x ^{2}} = 0

\frac{1}{3 x + 3} = \frac{1}{6} - \frac{2}{x + 1}

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