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

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

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

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

x = - \frac{1}{2}

Decimal Notation

x = - 0.5

Solution steps

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

Multiply by LCM

x + 2 x (x - 4) = 4

Solve

x + 2 x (x - 4) = 4 : x = 4, x = - \frac{1}{2}

x = 4, x = - \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = 4, x = 0

Since the equation is undefined for:

4

x = - \frac{1}{2}

1 - \frac{2}{x - 1} = \frac{2}{x ^{2} - 3 x + 2}

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

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

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

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

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