What is the answer to x/(x-2)-9/(2-x)=2 ?

The answer to x/(x-2)-9/(2-x)=2 is x=13

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x/(x-2)-9/(2-x)=2

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

x = 13

Solution steps

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

Multiply by LCM

x (- x + 2) - 9 (x - 2) = 2 (x - 2) (- x + 2)

Solve

x (- x + 2) - 9 (x - 2) = 2 (x - 2) (- x + 2) : x = 13, x = 2

x = 13, x = 2

Verify Solutions

Find undefined (singularity) points:

x = 2

Since the equation is undefined for:

2

x = 13

0 = 1 - \frac{16}{x ^{2}}

2 + \frac{1149984}{x ^{3}} = 66

1 - \frac{3}{2 x} = \frac{7}{4}

\frac{1}{x} + \frac{5}{x - 9} = 0

\frac{- 2}{3 x + 15} = - 20

What is the answer to x/(x-2)-9/(2-x)=2 ?
The answer to x/(x-2)-9/(2-x)=2 is x=13
Solve for x: x/(x-2)-9/(2-x)=2
The solution is x=13