Solve x-1/x+3=x+5/x-2

$$\frac { x - 1 } { x + 3 } = \frac { x + 5 } { x - 2 }$$

Solve for x

$$x = -\frac{13}{11} = -1\frac{2}{11} \approx -1.181818182$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+3\right), the least common multiple of x+3,x-2.

$$\left(x-2\right)\left(x-1\right)=\left(x+3\right)\left(x+5\right)$$

Use the distributive property to multiply x-2 by x-1 and combine like terms.

$$x^{2}-3x+2=\left(x+3\right)\left(x+5\right)$$

Use the distributive property to multiply x+3 by x+5 and combine like terms.

$$x^{2}-3x+2=x^{2}+8x+15$$

Subtract x^{2} from both sides.

$$x^{2}-3x+2-x^{2}=8x+15$$

Combine x^{2} and -x^{2} to get 0.

$$-3x+2=8x+15$$

Subtract 8x from both sides.

$$-3x+2-8x=15$$

Combine -3x and -8x to get -11x.

$$-11x+2=15$$

Subtract 2 from both sides.

$$-11x=15-2$$

Subtract 2 from 15 to get 13.

$$-11x=13$$

Divide both sides by -11.

$$x=\frac{13}{-11}$$

Fraction \frac{13}{-11} can be rewritten as -\frac{13}{11} by extracting the negative sign.

$$x=-\frac{13}{11}$$