Solve frac{x+sqrt{x}}{x^2+5x+6}=0

$$\frac { x + \sqrt { x } } { x ^ { 2 } + 5 x + 6 } = 0$$

Solve for x

$$x=0$$

Solution Steps

Variable x cannot be equal to any of the values -3,-2 since division by zero is not defined. Multiply both sides of the equation by \left(x+2\right)\left(x+3\right).

$$x+\sqrt{x}=0$$

Subtract x from both sides of the equation.

$$\sqrt{x}=-x$$

Square both sides of the equation.

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

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

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

Expand \left(-x\right)^{2}.

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

Calculate -1 to the power of 2 and get 1.

$$x=1x^{2}$$

Subtract 1x^{2} from both sides.

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

Factor out x.

$$x\left(1-x\right)=0$$

To find equation solutions, solve x=0 and 1-x=0.

$$x=0 x=1$$

Substitute 0 for x in the equation \frac{x+\sqrt{x}}{x^{2}+5x+6}=0.

$$\frac{0+\sqrt{0}}{0^{2}+5\times 0+6}=0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 1 for x in the equation \frac{x+\sqrt{x}}{x^{2}+5x+6}=0.

$$\frac{1+\sqrt{1}}{1^{2}+5\times 1+6}=0$$

Simplify. The value x=1 does not satisfy the equation.

$$\frac{1}{6}=0$$

Equation \sqrt{x}=-x has a unique solution.

$$x=0$$