Solve 5/x^2+3x-1/x^2-x=0

$$\frac { 5 } { x ^ { 2 } + 3 x } - \frac { 1 } { x ^ { 2 } - x } = 0$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,0,1 since division by zero is not defined. Multiply both sides of the equation by x\left(x-1\right)\left(x+3\right), the least common multiple of x^{2}+3x,x^{2}-x.

$$\left(x-1\right)\times 5-\left(x+3\right)=0$$

Use the distributive property to multiply x-1 by 5.

$$5x-5-\left(x+3\right)=0$$

To find the opposite of x+3, find the opposite of each term.

$$5x-5-x-3=0$$

Combine 5x and -x to get 4x.

$$4x-5-3=0$$

Subtract 3 from -5 to get -8.

$$4x-8=0$$

Add 8 to both sides. Anything plus zero gives itself.

$$4x=8$$

Divide both sides by 4.

$$x=\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$x=2$$