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

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

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

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

x = - \frac{4}{3}

Decimal Notation

x = - 1.33333 \dots

Solution steps

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

Cross multiply

x^{2} - 2 x = x^{2} + 7 x + 12

Subtract

x^{2} + 7 x

from both sides

x^{2} - 2 x - (x^{2} + 7 x) = x^{2} + 7 x + 12 - (x^{2} + 7 x)

Simplify

- 9 x = 12

Divide both sides by

- 9

x = - \frac{4}{3}

Verify Solutions

Find undefined (singularity) points:

x = - 3, x = 2

Combine undefined points with solutions:

x = - \frac{4}{3}

\frac{1}{18} = \frac{5}{- 4 ( x - 1 )}

\frac{2 π}{b} = \frac{π}{4}

\frac{12}{2 x} = 3

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

\frac{( x ^{2} + 3 x + 1 )}{( x + 1 )} = x

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