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

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

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

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

x = - \frac{1}{2}

Decimal

x = - 0.5

Solution steps

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

Cross multiply

x^{2} + 3 x - 10 = x^{2} - x - 12

Move

10

to the right side

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

Subtract

x^{2} - x

from both sides

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

Simplify

4 x = - 2

Divide both sides by

4

x = - \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = - 3, x = - 5

Combine undefined points with solutions:

x = - \frac{1}{2}

y, x + \frac{1}{x} = y + \frac{1}{y}

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

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

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

\frac{5}{3 n - 8} = \frac{n}{n + 2}

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