What is the answer to 1/x+1/(x-3)= 2/(x-4) ?

The answer to 1/x+1/(x-3)= 2/(x-4) is x= 12/5

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1/x+1/(x-3)= 2/(x-4)

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

x = \frac{12}{5}

Decimal Notation

x = 2.4

Solution steps

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

Multiply by LCM

2 x^{2} - 11 x + 12 = 2 x^{2} - 6 x

Move

12

to the right side

2 x^{2} - 11 x = 2 x^{2} - 6 x - 12

Subtract

2 x^{2} - 6 x

from both sides

2 x^{2} - 11 x - (2 x^{2} - 6 x) = 2 x^{2} - 6 x - 12 - (2 x^{2} - 6 x)

Simplify

- 5 x = - 12

Divide both sides by

- 5

x = \frac{12}{5}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 3, x = 4

Combine undefined points with solutions:

x = \frac{12}{5}

\frac{x - 14}{x - 15} = \frac{14}{13}

\frac{2369}{( x + 76 )} = 23

f, f (x - 3) = \frac{3}{x - 3}

\frac{1}{x} - \frac{3}{7 x} = \frac{8}{21}

\frac{k}{α} \cdot \frac{0.25}{20} = 10

What is the answer to 1/x+1/(x-3)= 2/(x-4) ?
The answer to 1/x+1/(x-3)= 2/(x-4) is x= 12/5
Solve for x: 1/x+1/(x-3)= 2/(x-4)
The solution is x= 12/5