What is the answer to (6x)/(x-1)+2= 6/(x^2-x) ?

The answer to (6x)/(x-1)+2= 6/(x^2-x) is x=-3/4

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(6x)/(x-1)+2= 6/(x^2-x)

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

x = - \frac{3}{4}

Decimal Notation

x = - 0.75

Solution steps

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

Multiply by LCM

6 x^{2} + 2 x (x - 1) = 6

Solve

6 x^{2} + 2 x (x - 1) = 6 : x = 1, x = - \frac{3}{4}

x = 1, x = - \frac{3}{4}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Since the equation is undefined for:

1

x = - \frac{3}{4}

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

\frac{1}{3} - \frac{1}{x} = \frac{5}{6}

\frac{3 - x}{9 x - 2} = 1

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

\frac{3}{x - 5} = 6

What is the answer to (6x)/(x-1)+2= 6/(x^2-x) ?
The answer to (6x)/(x-1)+2= 6/(x^2-x) is x=-3/4
Solve for x: (6x)/(x-1)+2= 6/(x^2-x)
The solution is x=-3/4