What is the answer to x/(x-3)= 5/(x-3)-1/2 ?

The answer to x/(x-3)= 5/(x-3)-1/2 is x= 13/3

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x/(x-3)= 5/(x-3)-1/2

\frac{x}{x - 3} = \frac{5}{x - 3} - \frac{1}{2}

x = \frac{13}{3}

Decimal Notation

x = 4.33333 \dots

Solution steps

\frac{x}{x - 3} = \frac{5}{x - 3} - \frac{1}{2}

Multiply by LCM

2 x = - x + 13

Move

x

to the left side

3 x = 13

Divide both sides by

3

x = \frac{13}{3}

Verify Solutions

Find undefined (singularity) points:

x = 3

Combine undefined points with solutions:

x = \frac{13}{3}

\frac{4}{( x - 2 ) ^{2}} - 1 = 0

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

x, 16 = \frac{1 - x}{x ^{2}}

\frac{4}{x} - \frac{5}{x + 3} = 1

\frac{3 x - 4}{x - 5} = \frac{3 x + 6}{x + 2}

What is the answer to x/(x-3)= 5/(x-3)-1/2 ?
The answer to x/(x-3)= 5/(x-3)-1/2 is x= 13/3
Solve for x: x/(x-3)= 5/(x-3)-1/2
The solution is x= 13/3