What is the answer to 1/(x^2-5x)=(x+7)/x-1 ?

The answer to 1/(x^2-5x)=(x+7)/x-1 is x= 36/7

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1/(x^2-5x)=(x+7)/x-1

\frac{1}{x ^{2} - 5 x} = \frac{x + 7}{x} - 1

x = \frac{36}{7}

Decimal Notation

x = 5.14285 \dots

Solution steps

\frac{1}{x ^{2} - 5 x} = \frac{x + 7}{x} - 1

Multiply by LCM

1 = (x + 7) (x - 5) - x (x - 5)

Switch sides

(x + 7) (x - 5) - x (x - 5) = 1

Expand

(x + 7) (x - 5) - x (x - 5) : 7 x - 35

7 x - 35 = 1

Move

35

to the right side

7 x = 36

Divide both sides by

7

x = \frac{36}{7}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 5

Combine undefined points with solutions:

x = \frac{36}{7}

\frac{0.25}{3} = \frac{12}{x}

\frac{6}{y} = \frac{9}{33}

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

\frac{9}{- t - 6} = \frac{27}{2 t + 22}

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

What is the answer to 1/(x^2-5x)=(x+7)/x-1 ?
The answer to 1/(x^2-5x)=(x+7)/x-1 is x= 36/7
Solve for x: 1/(x^2-5x)=(x+7)/x-1
The solution is x= 36/7