What is the answer to (2x+2)/(x-1)-6/x =2 ?

The answer to (2x+2)/(x-1)-6/x =2 is x=3

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(2x+2)/(x-1)-6/x =2

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

x = 3

Solution steps

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

Multiply by LCM

x (2 x + 2) - 6 (x - 1) = 2 x (x - 1)

Expand

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

2 x^{2} + 2 x - 6 (x - 1) = 2 x (x - 1)

Expand

- 6 (x - 1) : - 6 x + 6

2 x^{2} + 2 x - 6 x + 6 = 2 x (x - 1)

Add similar elements:

2 x - 6 x = - 4 x

2 x^{2} - 4 x + 6 = 2 x (x - 1)

Expand

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

2 x^{2} - 4 x + 6 = 2 x^{2} - 2 x

Move

6

to the right side

2 x^{2} - 4 x = 2 x^{2} - 2 x - 6

Subtract

2 x^{2} - 2 x

from both sides

2 x^{2} - 4 x - (2 x^{2} - 2 x) = 2 x^{2} - 2 x - 6 - (2 x^{2} - 2 x)

Simplify

- 2 x = - 6

Divide both sides by

- 2

x = 3

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Combine undefined points with solutions:

x = 3

- \frac{9}{x} + 2 x = - 7

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

x + \frac{9}{x} = - 10

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

\frac{1}{x ^{2}} + \frac{3}{x} - 10 = 0

What is the answer to (2x+2)/(x-1)-6/x =2 ?
The answer to (2x+2)/(x-1)-6/x =2 is x=3
Solve for x: (2x+2)/(x-1)-6/x =2
The solution is x=3