Solve x-1/8x=x^2+6x+5/8x^2-1/x

$$\frac { x - 1 } { 8 x } = \frac { x ^ { 2 } + 6 x + 5 } { 8 x ^ { 2 } } - \frac { 1 } { x }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 8x^{2}, the least common multiple of 8x,8x^{2},x.

$$x\left(x-1\right)=x^{2}+6x+5-8x$$

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

$$x^{2}-x=x^{2}+6x+5-8x$$

Combine 6x and -8x to get -2x.

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

Subtract x^{2} from both sides.

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

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

$$-x=-2x+5$$

Add 2x to both sides.

$$-x+2x=5$$

Combine -x and 2x to get x.

$$x=5$$