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

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

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

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

x = \frac{5}{3}

Decimal Notation

x = 1.66666 \dots

Solution steps

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

Multiply by LCM

2 x + 2 (x - 5) = x - 5

Expand

2 (x - 5) : 2 x - 10

2 x + 2 x - 10 = x - 5

Add similar elements:

2 x + 2 x = 4 x

4 x - 10 = x - 5

Move

10

to the right side

4 x = x + 5

Move

x

to the left side

3 x = 5

Divide both sides by

3

x = \frac{5}{3}

Verify Solutions

Find undefined (singularity) points:

x = 5

Combine undefined points with solutions:

x = \frac{5}{3}

- 3 = \frac{60}{2 - x}

\frac{x}{x - 8} + 3 = - \frac{4}{x - 8}

u, r = \frac{s - t}{u - 8}

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

\frac{4}{x} - 6 = - \frac{11}{5}