Solve 1/x=x+2-x^2-4x-5/x

$$\frac { 1 } { x } = x + 2 - \frac { x ^ { 2 } - 4 x - 5 } { x }$$

Solve for x

$$x=-\frac{2}{3}\approx -0.666666667$$

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 x.

$$1=xx+x\times 2-\left(x^{2}-4x-5\right)$$

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

$$1=x^{2}+x\times 2-\left(x^{2}-4x-5\right)$$

To find the opposite of x^{2}-4x-5, find the opposite of each term.

$$1=x^{2}+x\times 2-x^{2}+4x+5$$

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

$$1=x\times 2+4x+5$$

Combine x\times 2 and 4x to get 6x.

$$1=6x+5$$

Swap sides so that all variable terms are on the left hand side.

$$6x+5=1$$

Subtract 5 from both sides.

$$6x=1-5$$

Subtract 5 from 1 to get -4.

$$6x=-4$$

Divide both sides by 6.

$$x=\frac{-4}{6}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

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