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

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

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

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

x = 2

Solution steps

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

Cross multiply

x^{2} + 3 x - 18 = x^{2} - 2 x - 8

Move

18

to the right side

x^{2} + 3 x = x^{2} - 2 x + 10

Subtract

x^{2} - 2 x

from both sides

x^{2} + 3 x - (x^{2} - 2 x) = x^{2} - 2 x + 10 - (x^{2} - 2 x)

Simplify

5 x = 10

Divide both sides by

5

x = 2

Verify Solutions

Find undefined (singularity) points:

x = 4, x = - 6

Combine undefined points with solutions:

x = 2

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

x^{2} - 5 x - 2 - \frac{24}{x ^{2} - 5 x} = 0

\frac{9 x}{x + 9} + 1 = - \frac{1}{x + 9}

\frac{2}{y + 4} - \frac{1}{y - 3} = 0

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

What is the answer to (x-3)/(x-4)=(x+2)/(x+6) ?
The answer to (x-3)/(x-4)=(x+2)/(x+6) is x=2
Solve for x: (x-3)/(x-4)=(x+2)/(x+6)
The solution is x=2