Solve f(x)/2x-12=sqrt{3x-12}

$$\frac { f ( x ) } { 2 x - 12 } = \sqrt { 3 x - 12 }$$

Solve for f

$$f=-\frac{2\sqrt{3\left(x-4\right)}\left(6-x\right)}{x}$$

$$x\neq 6\text{ and }x\geq 4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(x-6\right).

$$fx=2\left(x-6\right)\sqrt{3x-12}$$

Use the distributive property to multiply 2 by x-6.

$$fx=\left(2x-12\right)\sqrt{3x-12}$$

Use the distributive property to multiply 2x-12 by \sqrt{3x-12}.

$$fx=2x\sqrt{3x-12}-12\sqrt{3x-12}$$

The equation is in standard form.

$$xf=2\sqrt{3x-12}x-12\sqrt{3x-12}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{2\sqrt{3x-12}\left(x-6\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{2\sqrt{3x-12}\left(x-6\right)}{x}$$