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

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

Solve for x

$$x=10$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,0,2 since division by zero is not defined. Multiply both sides of the equation by x\left(x-2\right)\left(x+2\right), the least common multiple of x,x+2,x-2.

$$\left(x^{2}-4\right)\times 5-x\left(x-2\right)\times 3=x\left(x+2\right)\times 2$$

Use the distributive property to multiply x^{2}-4 by 5.

$$5x^{2}-20-x\left(x-2\right)\times 3=x\left(x+2\right)\times 2$$

Use the distributive property to multiply x by x-2.

$$5x^{2}-20-\left(x^{2}-2x\right)\times 3=x\left(x+2\right)\times 2$$

Use the distributive property to multiply x^{2}-2x by 3.

$$5x^{2}-20-\left(3x^{2}-6x\right)=x\left(x+2\right)\times 2$$

To find the opposite of 3x^{2}-6x, find the opposite of each term.

$$5x^{2}-20-3x^{2}+6x=x\left(x+2\right)\times 2$$

Combine 5x^{2} and -3x^{2} to get 2x^{2}.

$$2x^{2}-20+6x=x\left(x+2\right)\times 2$$

Use the distributive property to multiply x by x+2.

$$2x^{2}-20+6x=\left(x^{2}+2x\right)\times 2$$

Use the distributive property to multiply x^{2}+2x by 2.

$$2x^{2}-20+6x=2x^{2}+4x$$

Subtract 2x^{2} from both sides.

$$2x^{2}-20+6x-2x^{2}=4x$$

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

$$-20+6x=4x$$

Subtract 4x from both sides.

$$-20+6x-4x=0$$

Combine 6x and -4x to get 2x.

$$-20+2x=0$$

Add 20 to both sides. Anything plus zero gives itself.

$$2x=20$$

Divide both sides by 2.

$$x=\frac{20}{2}$$

Divide 20 by 2 to get 10.

$$x=10$$