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

The answer to (5x)/(x-1)+7= 5/(x^2-x) is x=-5/12

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

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

x = - \frac{5}{12}

Decimal

x = - 0.41666 \dots

Solution steps

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

Multiply by LCM

5 x^{2} + 7 x (x - 1) = 5

Solve

5 x^{2} + 7 x (x - 1) = 5 : x = 1, x = - \frac{5}{12}

x = 1, x = - \frac{5}{12}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Since the equation is undefined for:

1

x = - \frac{5}{12}

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

4 π = \frac{2 π}{b}

8 x^{7} - \frac{8}{x ^{2}} = 0

\frac{9}{4 x ^{2}} + \frac{4}{x ^{2}} = 1

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

What is the answer to (5x)/(x-1)+7= 5/(x^2-x) ?
The answer to (5x)/(x-1)+7= 5/(x^2-x) is x=-5/12
Solve for x: (5x)/(x-1)+7= 5/(x^2-x)
The solution is x=-5/12