Solve 5/4f=5/sqrt{k-3}

$$\frac { 5 } { 4 } f = \frac { 5 } { \sqrt { k } - 3 }$$

Solve for f (complex solution)

$$f=\frac{4}{\sqrt{k}-3}$$

$$k\neq 9$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{5}{4}f=\frac{5}{\sqrt{k}-3}$$

Divide both sides of the equation by \frac{5}{4}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{4}f}{\frac{5}{4}}=\frac{5}{\frac{5}{4}\left(\sqrt{k}-3\right)}$$

Dividing by \frac{5}{4} undoes the multiplication by \frac{5}{4}.

$$f=\frac{5}{\frac{5}{4}\left(\sqrt{k}-3\right)}$$

Divide \frac{5}{-3+\sqrt{k}} by \frac{5}{4} by multiplying \frac{5}{-3+\sqrt{k}} by the reciprocal of \frac{5}{4}.

$$f=\frac{4}{\sqrt{k}-3}$$

Solve for f

$$f=\frac{4}{\sqrt{k}-3}$$

$$k\neq 9\text{ and }k\geq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{5}{4}f=\frac{5}{\sqrt{k}-3}$$

Divide both sides of the equation by \frac{5}{4}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{4}f}{\frac{5}{4}}=\frac{5}{\frac{5}{4}\left(\sqrt{k}-3\right)}$$

Dividing by \frac{5}{4} undoes the multiplication by \frac{5}{4}.

$$f=\frac{5}{\frac{5}{4}\left(\sqrt{k}-3\right)}$$

Divide \frac{5}{-3+\sqrt{k}} by \frac{5}{4} by multiplying \frac{5}{-3+\sqrt{k}} by the reciprocal of \frac{5}{4}.

$$f=\frac{4}{\sqrt{k}-3}$$

Solve for k (complex solution)

$$k=\left(3+\frac{4}{f}\right)^{2}$$

$$f\neq 0\text{ and }\left(arg(3+\frac{4}{f})<\pi \text{ or }f=-\frac{4}{3}\right)\text{ and }f\neq -\frac{2}{3}$$

Solve for k

$$k=\left(3+\frac{4}{f}\right)^{2}$$

$$f>0\text{ or }f\leq -\frac{4}{3}$$