What is the answer to 1/(x+2)+1/(x^2-2x)=8 ?

The answer to 1/(x+2)+1/(x^2-2x)=8 is x\approx-0.06472…,x\approx-1.87280…,x\approx 2.06252…

Solve for x: 1/(x+2)+1/(x^2-2x)=8

The solution is x\approx-0.06472…,x\approx-1.87280…,x\approx 2.06252…

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\frac{1}{x + 2} + \frac{1}{x ^{2} - 2 x} = 8

x \approx - 0.06472 \dots, x \approx - 1.87280 \dots, x \approx 2.06252 \dots

Solution steps

\frac{1}{x + 2} + \frac{1}{x ^{2} - 2 x} = 8

Multiply by LCM

x (x - 2) + x + 2 = 8 x (x + 2) (x - 2)

Solve

x (x - 2) + x + 2 = 8 x (x + 2) (x - 2) : x \approx - 0.06472 \dots, x \approx - 1.87280 \dots, x \approx 2.06252 \dots

x \approx - 0.06472 \dots, x \approx - 1.87280 \dots, x \approx 2.06252 \dots

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 2, x = 0

Combine undefined points with solutions:

x \approx - 0.06472 \dots, x \approx - 1.87280 \dots, x \approx 2.06252 \dots

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

\frac{5}{6 x} + \frac{1}{x} = - 4

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

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

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

What is the answer to 1/(x+2)+1/(x^2-2x)=8 ?
The answer to 1/(x+2)+1/(x^2-2x)=8 is x\approx-0.06472…,x\approx-1.87280…,x\approx 2.06252…
Solve for x: 1/(x+2)+1/(x^2-2x)=8
The solution is x\approx-0.06472…,x\approx-1.87280…,x\approx 2.06252…