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

The answer to (x-2)/(x+2)=(x+3)/(x-4) is x= 2/11

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

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

x = \frac{2}{11}

Decimal

x = 0.18181 \dots

Solution steps

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

Cross multiply

x^{2} - 6 x + 8 = x^{2} + 5 x + 6

Move

8

to the right side

x^{2} - 6 x = x^{2} + 5 x - 2

Subtract

x^{2} + 5 x

from both sides

x^{2} - 6 x - (x^{2} + 5 x) = x^{2} + 5 x - 2 - (x^{2} + 5 x)

Simplify

- 11 x = - 2

Divide both sides by

- 11

x = \frac{2}{11}

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 4

Combine undefined points with solutions:

x = \frac{2}{11}

\frac{8432 - 3870}{x} = 8346

\frac{28}{x - 36} = \frac{36}{x - 28}

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

y, x = z - \frac{z - y}{z + y}

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

What is the answer to (x-2)/(x+2)=(x+3)/(x-4) ?
The answer to (x-2)/(x+2)=(x+3)/(x-4) is x= 2/11
Solve for x: (x-2)/(x+2)=(x+3)/(x-4)
The solution is x= 2/11