Solve sqrt{2x^2+6x/x+3}=x

$$\sqrt { \frac { 2 x ^ { 2 } + 6 x } { x + 3 } } = x$$

Solve for x

$$x=2$$

$$x=0$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{\frac{2x^{2}+6x}{x+3}}\right)^{2}=x^{2}$$

Factor the expressions that are not already factored in \frac{2x^{2}+6x}{x+3}.

$$\left(\sqrt{\frac{2x\left(x+3\right)}{x+3}}\right)^{2}=x^{2}$$

Cancel out x+3 in both numerator and denominator.

$$\left(\sqrt{2x}\right)^{2}=x^{2}$$

Calculate \sqrt{2x} to the power of 2 and get 2x.

$$2x=x^{2}$$

Subtract x^{2} from both sides.

$$2x-x^{2}=0$$

Factor out x.

$$x\left(2-x\right)=0$$

To find equation solutions, solve x=0 and 2-x=0.

$$x=0 x=2$$

Substitute 0 for x in the equation \sqrt{\frac{2x^{2}+6x}{x+3}}=x.

$$\sqrt{\frac{2\times 0^{2}+6\times 0}{0+3}}=0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 2 for x in the equation \sqrt{\frac{2x^{2}+6x}{x+3}}=x.

$$\sqrt{\frac{2\times 2^{2}+6\times 2}{2+3}}=2$$

Simplify. The value x=2 satisfies the equation.

$$2=2$$

List all solutions of \sqrt{\frac{2x^{2}+6x}{x+3}}=x.

$$x=0 x=2$$