What is the answer to (10)/(x-5)+x=1+(2x)/(x-5) ?

The answer to (10)/(x-5)+x=1+(2x)/(x-5) is x=3

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

\frac{10}{x - 5} + x = 1 + \frac{2 x}{x - 5}

x = 3

Solution steps

\frac{10}{x - 5} + x = 1 + \frac{2 x}{x - 5}

Multiply both sides by

x - 5

10 + x (x - 5) = 3 x - 5

Solve

10 + x (x - 5) = 3 x - 5 : x = 5, x = 3

x = 5, x = 3

Verify Solutions

Find undefined (singularity) points:

x = 5

Since the equation is undefined for:

5

x = 3

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

\frac{x ^{2}}{4} = \frac{2}{x ^{2} + 1}

\frac{1}{4 x ^{2}} = \frac{1}{2 x - ( \frac{3}{4 x ^{2}} )}

7 - \frac{1}{x} = - 8 x

\frac{3 a}{2 a + 1} - \frac{4}{2 a - 1} = 1

What is the answer to (10)/(x-5)+x=1+(2x)/(x-5) ?
The answer to (10)/(x-5)+x=1+(2x)/(x-5) is x=3
Solve for x: (10)/(x-5)+x=1+(2x)/(x-5)
The solution is x=3