Solve x^2-12/x=x+5/3

$$\frac { x ^ { 2 } - 12 } { x } = x + \frac { 5 } { 3 }$$

Solve for x

$$x = -\frac{36}{5} = -7\frac{1}{5} = -7.2$$

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 3x, the least common multiple of x,3.

$$3\left(x^{2}-12\right)=3xx+3x\times \frac{5}{3}$$

Use the distributive property to multiply 3 by x^{2}-12.

$$3x^{2}-36=3xx+3x\times \frac{5}{3}$$

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

$$3x^{2}-36=3x^{2}+3x\times \frac{5}{3}$$

Multiply 3 and \frac{5}{3} to get 5.

$$3x^{2}-36=3x^{2}+5x$$

Subtract 3x^{2} from both sides.

$$3x^{2}-36-3x^{2}=5x$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-36=5x$$

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

$$5x=-36$$

Divide both sides by 5.

$$x=\frac{-36}{5}$$

Fraction \frac{-36}{5} can be rewritten as -\frac{36}{5} by extracting the negative sign.

$$x=-\frac{36}{5}$$