What is the answer to 6/(x+2)= 3/(x-4) ?

The answer to 6/(x+2)= 3/(x-4) is x=10

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

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

x = 10

Solution steps

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

Cross multiply

6 x - 24 = 3 x + 6

Move

24

to the right side

6 x = 3 x + 30

Move

3 x

to the left side

3 x = 30

Divide both sides by

3

x = 10

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 4

Combine undefined points with solutions:

x = 10

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

0 = x - 5 + \frac{4}{x}

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

\frac{32}{x} = 15

\frac{7}{4} = \frac{14}{x}