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

The answer to x/(2-x)=2-x is x=4,x=1

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x/(2-x)=2-x

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

x = 4, x = 1

Solution steps

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

Multiply both sides by

2 - x

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

Solve

x = 2 (2 - x) - x (2 - x) : x = 4, x = 1

x = 4, x = 1

Verify Solutions

Find undefined (singularity) points:

x = 2

Combine undefined points with solutions:

x = 4, x = 1

\frac{1}{2} - \frac{12}{x + 3} = 4

(y - 1) (y - 2) = \frac{1}{2 y ^{2}}

\frac{a x + b}{c x + d} = 9

\frac{a x + b}{c x + d} = 8

\frac{15}{2 x} + \frac{7}{x} = 1