Solve 1/sqrt{x}+1/-x9=1/20

$$\frac{ 1 }{ \sqrt{ x } } + \frac{ 1 }{ -x9 } = \frac{ 1 }{ 20 }$$

Solve for x_9

$$x_{9}=-\frac{20\sqrt{x}\left(\sqrt{x}+20\right)}{x-400}$$

$$x\neq 400\text{ and }x>0$$

Steps for Solving Linear Equation

Subtract \frac{1}{\sqrt{x}} from both sides.

$$\frac{1}{-x_{9}}=\frac{1}{20}-\frac{1}{\sqrt{x}}$$

Variable x_{9} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 20x_{9}, the least common multiple of -x_{9},20.

$$-20=20x_{9}\times \frac{1}{20}-20x_{9}x^{-\frac{1}{2}}$$

Multiply 20 and \frac{1}{20} to get 1.

$$-20=x_{9}-20x_{9}x^{-\frac{1}{2}}$$

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

$$x_{9}-20x_{9}x^{-\frac{1}{2}}=-20$$

Combine all terms containing x_{9}.

$$\left(1-20x^{-\frac{1}{2}}\right)x_{9}=-20$$

The equation is in standard form.

$$\left(1-\frac{20}{\sqrt{x}}\right)x_{9}=-20$$

Divide both sides by 1-20x^{-\frac{1}{2}}.

$$\frac{\left(1-\frac{20}{\sqrt{x}}\right)x_{9}}{1-\frac{20}{\sqrt{x}}}=-\frac{20}{1-\frac{20}{\sqrt{x}}}$$

Dividing by 1-20x^{-\frac{1}{2}} undoes the multiplication by 1-20x^{-\frac{1}{2}}.

$$x_{9}=-\frac{20}{1-\frac{20}{\sqrt{x}}}$$

Divide -20 by 1-20x^{-\frac{1}{2}}.

$$x_{9}=-\frac{20\sqrt{x}}{\sqrt{x}-20}$$

Variable x_{9} cannot be equal to 0.

$$x_{9}=-\frac{20\sqrt{x}}{\sqrt{x}-20}\text{, }x_{9}\neq 0$$

Solve for x

$$x=400\times \left(\frac{x_{9}}{x_{9}+20}\right)^{2}$$

$$x_{9}<-20\text{ or }x_{9}>0$$