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

The answer to (x-1)/(2-x)=2x+1 is x=-(-1+sqrt(7))/2 ,x=(1+sqrt(7))/2

Solve for x: (x-1)/(2-x)=2x+1

The solution is x=-(-1+sqrt(7))/2 ,x=(1+sqrt(7))/2

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

x = - \frac{- 1 + 7}{2}, x = \frac{1 + 7}{2}

Decimal Notation

x = - 0.82287 \dots, x = 1.82287 \dots

Solution steps

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

Multiply both sides by

2 - x

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

Solve

x - 1 = 2 x (2 - x) + 2 - x : x = - \frac{- 1 + 7}{2}, x = \frac{1 + 7}{2}

x = - \frac{- 1 + 7}{2}, x = \frac{1 + 7}{2}

Verify Solutions

Find undefined (singularity) points:

x = 2

Combine undefined points with solutions:

x = - \frac{- 1 + 7}{2}, x = \frac{1 + 7}{2}

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

\frac{12}{x} + x = 8

\frac{2 x}{x + 4} = 7 - \frac{8}{x + 4}

z, x = \frac{w + r ^{2}}{z}

\frac{36}{x} = \frac{9}{2}

What is the answer to (x-1)/(2-x)=2x+1 ?
The answer to (x-1)/(2-x)=2x+1 is x=-(-1+sqrt(7))/2 ,x=(1+sqrt(7))/2
Solve for x: (x-1)/(2-x)=2x+1
The solution is x=-(-1+sqrt(7))/2 ,x=(1+sqrt(7))/2