Solve sqrt{4-x}quadf(x)=1/sqrt{x+5}

$$\sqrt { 4 - x } \quad f ( x ) = \frac { 1 } { \sqrt { x + 5 } }$$

Solve for f (complex solution)

$$f=\frac{\left(4-x\right)^{-\frac{1}{2}}\left(x+5\right)^{-\frac{1}{2}}}{x}$$

$$x\neq -5\text{ and }x\neq 0\text{ and }x\neq 4$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\sqrt{4-x}xf=\frac{1}{\sqrt{x+5}}$$

Divide both sides by \sqrt{4-x}x.

$$\frac{\sqrt{4-x}xf}{\sqrt{4-x}x}=\frac{\left(x+5\right)^{-\frac{1}{2}}}{\sqrt{4-x}x}$$

Dividing by \sqrt{4-x}x undoes the multiplication by \sqrt{4-x}x.

$$f=\frac{\left(x+5\right)^{-\frac{1}{2}}}{\sqrt{4-x}x}$$

Divide \left(x+5\right)^{-\frac{1}{2}} by \sqrt{4-x}x.

$$f=\frac{\left(4-x\right)^{-\frac{1}{2}}\left(x+5\right)^{-\frac{1}{2}}}{x}$$

Solve for f

$$f=\frac{1}{x\sqrt{\left(4-x\right)\left(x+5\right)}}$$

$$x\neq 0\text{ and }x>-5\text{ and }x<4$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\sqrt{4-x}xf=\frac{1}{\sqrt{x+5}}$$

Divide both sides by \sqrt{4-x}x.

$$\frac{\sqrt{4-x}xf}{\sqrt{4-x}x}=\frac{1}{\sqrt{x+5}\sqrt{4-x}x}$$

Dividing by \sqrt{4-x}x undoes the multiplication by \sqrt{4-x}x.

$$f=\frac{1}{\sqrt{x+5}\sqrt{4-x}x}$$

Divide \frac{1}{\sqrt{x+5}} by \sqrt{4-x}x.

$$f=\frac{1}{x\sqrt{\left(4-x\right)\left(x+5\right)}}$$