What is the answer to (2x)/(x-2)-2=(-4)/(2-x) ?

The answer to (2x)/(x-2)-2=(-4)/(2-x) is x\ne 2

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(2x)/(x-2)-2=(-4)/(2-x)

\frac{2 x}{x - 2} - 2 = \frac{- 4}{2 - x}

x \neq = 2

Solution steps

\frac{2 x}{x - 2} - 2 = \frac{- 4}{2 - x}

Multiply by LCM

2 x (- x + 2) - 2 (x - 2) (- x + 2) = - 4 (x - 2)

Solve

2 x (- x + 2) - 2 (x - 2) (- x + 2) = - 4 (x - 2) :

True for all

x

x \neq = 2

Verify Solutions

Find undefined (singularity) points:

x = 2

Since the equation is undefined for:

2

x \neq = 2

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

x - \frac{3}{x - 9} = \frac{7}{x - 9}

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

\frac{x + 1}{x} = 4

\frac{x - 12}{x - 4} = \frac{3}{5}

What is the answer to (2x)/(x-2)-2=(-4)/(2-x) ?
The answer to (2x)/(x-2)-2=(-4)/(2-x) is x\ne 2
Solve for x: (2x)/(x-2)-2=(-4)/(2-x)
The solution is x\ne 2