What is the answer to (x^2-4x)/(x-2)=1+4/(2-x) ?

The answer to (x^2-4x)/(x-2)=1+4/(2-x) is x=3

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(x^2-4x)/(x-2)=1+4/(2-x)

\frac{x ^{2} - 4 x}{x - 2} = 1 + \frac{4}{2 - x}

x = 3

Solution steps

\frac{x ^{2} - 4 x}{x - 2} = 1 + \frac{4}{2 - x}

Multiply by LCM

(x^{2} - 4 x) (- x + 2) = (x - 2) (- x + 2) + 4 (x - 2)

Solve

(x^{2} - 4 x) (- x + 2) = (x - 2) (- x + 2) + 4 (x - 2) : x = 2, x = 3

x = 2, x = 3

Verify Solutions

Find undefined (singularity) points:

x = 2

Since the equation is undefined for:

2

x = 3

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

5 - \frac{1600}{x ^{2}} = 0

3 - \frac{x}{x + 3} = \frac{1}{x + 3}

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

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

What is the answer to (x^2-4x)/(x-2)=1+4/(2-x) ?
The answer to (x^2-4x)/(x-2)=1+4/(2-x) is x=3
Solve for x: (x^2-4x)/(x-2)=1+4/(2-x)
The solution is x=3