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

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

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

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

x = - \frac{1}{4}

Decimal Notation

x = - 0.25

Solution steps

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

Multiply by LCM

x + 4 x (x - 1) = 1

Solve

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

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

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Since the equation is undefined for:

1

x = - \frac{1}{4}

- \frac{7}{( x - 4 ) ^{2}} = 0

7 x + \frac{x}{x - 9} = \frac{9}{x - 9}

\frac{x}{x + 5} + 4 = - \frac{5}{x + 5}

y, y + \frac{1}{x - 2} = 15

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

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