Solve x/x-3-8/x+5=x^2/x^2+2x-15

$$\frac { x } { x - 3 } - \frac { 8 } { x + 5 } = \frac { x ^ { 2 } } { x ^ { 2 } + 2 x - 15 }$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+5\right), the least common multiple of x-3,x+5,x^{2}+2x-15.

$$\left(x+5\right)x-\left(x-3\right)\times 8=x^{2}$$

Use the distributive property to multiply x+5 by x.

$$x^{2}+5x-\left(x-3\right)\times 8=x^{2}$$

Use the distributive property to multiply x-3 by 8.

$$x^{2}+5x-\left(8x-24\right)=x^{2}$$

To find the opposite of 8x-24, find the opposite of each term.

$$x^{2}+5x-8x+24=x^{2}$$

Combine 5x and -8x to get -3x.

$$x^{2}-3x+24=x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-3x+24-x^{2}=0$$

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

$$-3x+24=0$$

Subtract 24 from both sides. Anything subtracted from zero gives its negation.

$$-3x=-24$$

Divide both sides by -3.

$$x=\frac{-24}{-3}$$

Divide -24 by -3 to get 8.

$$x=8$$