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

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

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

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

x = \frac{1}{7}

Decimal Notation

x = 0.14285 \dots

Solution steps

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

Multiply by LCM

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

Solve

- x + 7 x (x - 1) = - 1 : x = 1, x = \frac{1}{7}

x = 1, x = \frac{1}{7}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Since the equation is undefined for:

1

x = \frac{1}{7}

\frac{10 x ^{2} - 5 x + 8}{5 x ^{2} + 9 x - 19} = 2

x, z = \frac{y}{x}

\frac{4}{2 x - 1} = 10

\frac{22}{x} = \frac{88}{100}

\frac{2 t}{( 4 - t ^{2} ) ^{2}} = 0

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