Solve ay/ax=6xsqrt{x}

$$\frac { a y } { a x } = 6 x \sqrt { x }$$

Solve for a

$$a\neq 0$$

$$y=6x^{\frac{5}{2}}\text{ and }x>0$$

Steps for Solving Linear Equation

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

$$ay=6x\sqrt{x}ax$$

Multiply x and x to get x^{2}.

$$ay=6x^{2}\sqrt{x}a$$

Subtract 6x^{2}\sqrt{x}a from both sides.

$$ay-6x^{2}\sqrt{x}a=0$$

Combine all terms containing a.

$$\left(y-6x^{2}\sqrt{x}\right)a=0$$

The equation is in standard form.

$$\left(-6\sqrt{x}x^{2}+y\right)a=0$$

Divide 0 by y-6x^{2}\sqrt{x}.

$$a=0$$

Variable a cannot be equal to 0.

$$a\in \emptyset$$

Solve for x

$$x=\frac{6^{\frac{3}{5}}y^{\frac{2}{5}}}{6}$$

$$a\neq 0\text{ and }y>0$$