What is the answer to -(3-x)/(x+2)+(x-1)/(x-2)=2 ?

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

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

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

x = 3

Solution steps

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

Multiply by LCM

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

Expand

(x + 2) (x - 2) : x^{2} - 4

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

Expand

2 (x^{2} - 4) : 2 x^{2} - 8

2 x^{2} - 4 x + 4 = 2 x^{2} - 8

Expand

- (3 - x) (x - 2) + (x - 1) (x + 2) : 2 x^{2} - 4 x + 4

2 x^{2} - 4 x + 4 = 2 x^{2} - 8

Move

4

to the right side

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

Move

2 x^{2}

to the left side

- 4 x = - 12

Divide both sides by

- 4

x = 3

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 2

Combine undefined points with solutions:

x = 3

\frac{1}{x - 1} + \frac{2}{x} = 0

\frac{4}{3 + z} = \frac{6}{5}

x^{2} + \frac{5}{x} = 8

5 x^{- 3} = 135

9 - \frac{6 x}{x + 4} = - \frac{3}{x + 4}

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