What is the answer to (x^2-5x+1)/(x-2)=x ?

The answer to (x^2-5x+1)/(x-2)=x is x= 1/3

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(x^2-5x+1)/(x-2)=x

\frac{x ^{2} - 5 x + 1}{x - 2} = x

x = \frac{1}{3}

Decimal Notation

x = 0.33333 \dots

Solution steps

\frac{x ^{2} - 5 x + 1}{x - 2} = x

Multiply both sides by

x - 2

x^{2} - 5 x + 1 = x (x - 2)

Expand

x (x - 2) : x^{2} - 2 x

x^{2} - 5 x + 1 = x^{2} - 2 x

Move

1

to the right side

x^{2} - 5 x = x^{2} - 2 x - 1

Subtract

x^{2} - 2 x

from both sides

x^{2} - 5 x - (x^{2} - 2 x) = x^{2} - 2 x - 1 - (x^{2} - 2 x)

Simplify

- 3 x = - 1

Divide both sides by

- 3

x = \frac{1}{3}

Verify Solutions

Find undefined (singularity) points:

x = 2

Combine undefined points with solutions:

x = \frac{1}{3}

\frac{3}{y - 2} - 2 = \frac{1}{y - 1}

\frac{11}{2} = \frac{33}{x}

0.9 = \frac{2.47 x}{1 + 1.47 x}

\frac{4}{x} = 0

\frac{4}{x} = 2

What is the answer to (x^2-5x+1)/(x-2)=x ?
The answer to (x^2-5x+1)/(x-2)=x is x= 1/3
Solve for x: (x^2-5x+1)/(x-2)=x
The solution is x= 1/3