What is the answer to 9+2/(x-1)=-4/(x-2) ?

The answer to 9+2/(x-1)=-4/(x-2) is x= 5/3 ,x= 2/3

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9+2/(x-1)=-4/(x-2)

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

x = \frac{5}{3}, x = \frac{2}{3}

Solution steps

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

Multiply by LCM

9 (x - 1) (x - 2) + 2 (x - 2) = - 4 (x - 1)

Solve

9 (x - 1) (x - 2) + 2 (x - 2) = - 4 (x - 1) : x = \frac{5}{3}, x = \frac{2}{3}

x = \frac{5}{3}, x = \frac{2}{3}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 2

Combine undefined points with solutions:

x = \frac{5}{3}, x = \frac{2}{3}

\frac{x + 2}{x - 1} = 0

\frac{3}{x ^{2} + 5 x} = \frac{1}{2}

\frac{3}{x} = \frac{2}{3}

x + \frac{10}{x} = 6

\frac{3}{x - 2} = \frac{2}{x + 5}

What is the answer to 9+2/(x-1)=-4/(x-2) ?
The answer to 9+2/(x-1)=-4/(x-2) is x= 5/3 ,x= 2/3
Solve for x: 9+2/(x-1)=-4/(x-2)
The solution is x= 5/3 ,x= 2/3