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

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

Solve for x

$$x=\frac{1}{8}=0.125$$

Steps for Solving Linear Equation

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

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

Multiply x and x to get x^{2}.

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

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

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

Subtract x^{2} from both sides.

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

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

$$5x-1=-3x$$

Add 3x to both sides.

$$5x-1+3x=0$$

Combine 5x and 3x to get 8x.

$$8x-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$8x=1$$

Divide both sides by 8.

$$x=\frac{1}{8}$$