What is the answer to x/(x-3)+8= 9/(x^2-3x) ?

The answer to x/(x-3)+8= 9/(x^2-3x) is x=-1/3

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x/(x-3)+8= 9/(x^2-3x)

\frac{x}{x - 3} + 8 = \frac{9}{x ^{2} - 3 x}

x = - \frac{1}{3}

Decimal Notation

x = - 0.33333 \dots

Solution steps

\frac{x}{x - 3} + 8 = \frac{9}{x ^{2} - 3 x}

Multiply by LCM

x^{2} + 8 x (x - 3) = 9

Solve

x^{2} + 8 x (x - 3) = 9 : x = 3, x = - \frac{1}{3}

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

Verify Solutions

Find undefined (singularity) points:

x = 3, x = 0

Since the equation is undefined for:

3

x = - \frac{1}{3}

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

8 x + \frac{x}{x - 8} = \frac{8}{x - 8}

\frac{2 z}{z + 3} = \frac{3}{z - 10} + 2

\frac{5}{x + 4} = \frac{3}{x - 2}

\frac{z ^{6} + 1}{z ^{2} + 1} = 0

What is the answer to x/(x-3)+8= 9/(x^2-3x) ?
The answer to x/(x-3)+8= 9/(x^2-3x) is x=-1/3
Solve for x: x/(x-3)+8= 9/(x^2-3x)
The solution is x=-1/3