What is the answer to x/(x-2)-5/(x+1)=1 ?

The answer to x/(x-2)-5/(x+1)=1 is x=4

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x/(x-2)-5/(x+1)=1

\frac{x}{x - 2} - \frac{5}{x + 1} = 1

x = 4

Solution steps

\frac{x}{x - 2} - \frac{5}{x + 1} = 1

Multiply by LCM

x (x + 1) - 5 (x - 2) = (x - 2) (x + 1)

Expand

x (x + 1) : x^{2} + x

x^{2} + x - 5 (x - 2) = (x - 2) (x + 1)

Expand

- 5 (x - 2) : - 5 x + 10

x^{2} + x - 5 x + 10 = (x - 2) (x + 1)

Add similar elements:

x - 5 x = - 4 x

x^{2} - 4 x + 10 = (x - 2) (x + 1)

Expand

(x - 2) (x + 1) : x^{2} - x - 2

x^{2} - 4 x + 10 = x^{2} - x - 2

Move

10

to the right side

x^{2} - 4 x = x^{2} - x - 12

Subtract

x^{2} - x

from both sides

x^{2} - 4 x - (x^{2} - x) = x^{2} - x - 12 - (x^{2} - x)

Simplify

- 3 x = - 12

Divide both sides by

- 3

x = 4

Verify Solutions

Find undefined (singularity) points:

x = 2, x = - 1

Combine undefined points with solutions:

x = 4

3 = \frac{a - ( - 3 )}{5 - a}

\frac{1}{x ^{2}} = \frac{1}{4}

\frac{( 2 x + 20 )}{2 x} = 5 x - 4

\frac{2}{x + 2} + \frac{5}{3 x} = 4 x

\frac{2}{x} = \frac{x}{8}

What is the answer to x/(x-2)-5/(x+1)=1 ?
The answer to x/(x-2)-5/(x+1)=1 is x=4
Solve for x: x/(x-2)-5/(x+1)=1
The solution is x=4