What is the answer to 2/(x-2)+3/x = 5/(x-4) ?

The answer to 2/(x-2)+3/x = 5/(x-4) is x= 3/2

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2/(x-2)+3/x = 5/(x-4)

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

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

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

Multiply by LCM

5 x^{2} - 26 x + 24 = 5 x^{2} - 10 x

Move

24

to the right side

5 x^{2} - 26 x = 5 x^{2} - 10 x - 24

Subtract

5 x^{2} - 10 x

from both sides

5 x^{2} - 26 x - (5 x^{2} - 10 x) = 5 x^{2} - 10 x - 24 - (5 x^{2} - 10 x)

Simplify

- 16 x = - 24

Divide both sides by

- 16

x = \frac{3}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 2, x = 4

Combine undefined points with solutions:

x = \frac{3}{2}

\frac{9}{- 3 x} = \frac{12}{x + 10}

\frac{6}{x + 7} = \frac{8}{x}

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

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

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

What is the answer to 2/(x-2)+3/x = 5/(x-4) ?
The answer to 2/(x-2)+3/x = 5/(x-4) is x= 3/2
Solve for x: 2/(x-2)+3/x = 5/(x-4)
The solution is x= 3/2