Solve -frac{sqrt{4}}{x^2+7}=y

$$- \frac { \sqrt { 4 } } { x ^ { 2 } + 7 } = y$$

Solve for y (complex solution)

$$y=-\frac{2}{x^{2}+7}$$

$$x\neq -\sqrt{7}i\text{ and }x\neq \sqrt{7}i$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}+7.

$$-\sqrt{4}=y\left(x^{2}+7\right)$$

Calculate the square root of 4 and get 2.

$$-2=y\left(x^{2}+7\right)$$

Use the distributive property to multiply y by x^{2}+7.

$$-2=yx^{2}+7y$$

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

$$yx^{2}+7y=-2$$

Combine all terms containing y.

$$\left(x^{2}+7\right)y=-2$$

Divide both sides by x^{2}+7.

$$\frac{\left(x^{2}+7\right)y}{x^{2}+7}=-\frac{2}{x^{2}+7}$$

Dividing by x^{2}+7 undoes the multiplication by x^{2}+7.

$$y=-\frac{2}{x^{2}+7}$$

Solve for y

$$y=-\frac{2}{x^{2}+7}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}+7.

$$-\sqrt{4}=y\left(x^{2}+7\right)$$

Calculate the square root of 4 and get 2.

$$-2=y\left(x^{2}+7\right)$$

Use the distributive property to multiply y by x^{2}+7.

$$-2=yx^{2}+7y$$

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

$$yx^{2}+7y=-2$$

Combine all terms containing y.

$$\left(x^{2}+7\right)y=-2$$

Divide both sides by x^{2}+7.

$$\frac{\left(x^{2}+7\right)y}{x^{2}+7}=-\frac{2}{x^{2}+7}$$

Dividing by x^{2}+7 undoes the multiplication by x^{2}+7.

$$y=-\frac{2}{x^{2}+7}$$

Solve for x (complex solution)

$$x=-\sqrt{-7-\frac{2}{y}}$$

$$x=\sqrt{-7-\frac{2}{y}}\text{, }y\neq 0$$

Solve for x

$$x=\sqrt{-7-\frac{2}{y}}$$

$$x=-\sqrt{-7-\frac{2}{y}}\text{, }y\geq -\frac{2}{7}\text{ and }y<0$$