Solve y^2=5/x+2

$${ y }^{ 2 } = \frac{ 5 }{ x+2 }$$

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by x+2.

$$\left(x+2\right)y^{2}=5$$

Use the distributive property to multiply x+2 by y^{2}.

$$xy^{2}+2y^{2}=5$$

Subtract 2y^{2} from both sides.

$$xy^{2}=5-2y^{2}$$

The equation is in standard form.

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

Divide both sides by y^{2}.

$$\frac{y^{2}x}{y^{2}}=\frac{5-2y^{2}}{y^{2}}$$

Dividing by y^{2} undoes the multiplication by y^{2}.

$$x=\frac{5-2y^{2}}{y^{2}}$$

Divide 5-2y^{2} by y^{2}.

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

Variable x cannot be equal to -2.

$$x=-2+\frac{5}{y^{2}}\text{, }x\neq -2$$

Solve for y (complex solution)

$$y=-\sqrt{5}\left(x+2\right)^{-\frac{1}{2}}$$

$$y=\sqrt{5}\left(x+2\right)^{-\frac{1}{2}}\text{, }x\neq -2$$

Solve for y

$$y=\sqrt{\frac{5}{x+2}}$$

$$y=-\sqrt{\frac{5}{x+2}}\text{, }x>-2$$