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

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

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

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

x = - \frac{1}{5}

Decimal Notation

x = - 0.2

Solution steps

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

Multiply by LCM

x + 5 x (x - 5) = 5

Solve

x + 5 x (x - 5) = 5 : x = 5, x = - \frac{1}{5}

x = 5, x = - \frac{1}{5}

Verify Solutions

Find undefined (singularity) points:

x = 5, x = 0

Since the equation is undefined for:

5

x = - \frac{1}{5}

\frac{1}{3 x} + \frac{1}{4 x} = 720

\frac{7}{x + 1} = \frac{4 x - 6}{2 x - 3}

\frac{21}{a + 2} = \frac{3}{a - 1}

\frac{x + 2}{x ^{2} - 3 x} = 0

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

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