Solve h^-1(x)=2/x+7

$$h ^ { - 1 } ( x ) = \frac { 2 } { x + 7 }$$

Solve for h

$$h=\frac{x\left(x+7\right)}{2}$$

$$x\neq -7\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+7.

$$h^{-1}x\left(x+7\right)=2$$

Use the distributive property to multiply h^{-1}x by x+7.

$$h^{-1}x^{2}+7h^{-1}x=2$$

Reorder the terms.

$$\frac{1}{h}x^{2}+7\times \frac{1}{h}x=2$$

Variable h cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by h.

$$1x^{2}+7\times 1x=2h$$

Multiply 7 and 1 to get 7.

$$1x^{2}+7x=2h$$

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

$$2h=1x^{2}+7x$$

Reorder the terms.

$$2h=x^{2}+7x$$

Divide both sides by 2.

$$\frac{2h}{2}=\frac{x\left(x+7\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$h=\frac{x\left(x+7\right)}{2}$$

Variable h cannot be equal to 0.

$$h=\frac{x\left(x+7\right)}{2}\text{, }h\neq 0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{8h+49}-7}{2}$$

$$x=\frac{-\sqrt{8h+49}-7}{2}\text{, }h\neq 0$$

Solve for x

$$x=\frac{\sqrt{8h+49}-7}{2}$$

$$x=\frac{-\sqrt{8h+49}-7}{2}\text{, }h\neq 0\text{ and }h\geq -\frac{49}{8}$$