What is the answer to 1+x/(x-3)=-1/(x^2-3x) ?

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

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1+x/(x-3)=-1/(x^2-3x)

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

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

Decimal Notation

x = 1, x = 0.5

Solution steps

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

Multiply by LCM

x (x - 3) + x^{2} = - 1

Solve

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

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

Verify Solutions

Find undefined (singularity) points:

x = 3, x = 0

Combine undefined points with solutions:

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

y, 4 y = \frac{6 + x ^{5}}{x ^{5} y}

5 - \frac{400}{x ^{2}} = 0

\frac{x}{x + 1} - \frac{x - 1}{x} = \frac{1}{20}

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

\frac{6}{x} - \frac{1}{2 x} = \frac{5}{x ^{2}}

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