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

The answer to x/(x-2)+(2x)/(2-x)=-x is x=0,x=3

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

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

x = 0, x = 3

Solution steps

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

Multiply by LCM

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

Solve

x (- x + 2) + 2 x (x - 2) = - x (x - 2) (- x + 2) : x = 0, x = 2, x = 3

x = 0, x = 2, x = 3

Verify Solutions

Find undefined (singularity) points:

x = 2

Since the equation is undefined for:

2

x = 0, x = 3

\frac{4}{3 x} + \frac{7}{4} = 6 - \frac{5}{2 x}

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

\frac{1}{x ^{2}} - \frac{1}{( x + 1 ) ^{2}} = 1

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

y, x = \frac{y}{y + 1}

What is the answer to x/(x-2)+(2x)/(2-x)=-x ?
The answer to x/(x-2)+(2x)/(2-x)=-x is x=0,x=3
Solve for x: x/(x-2)+(2x)/(2-x)=-x
The solution is x=0,x=3