Solve =frac{frac{asqrt{3}}{8}}{a+a/2}=y

$$= \frac { \frac { a \sqrt { 3 } } { 8 } } { a + \frac { a } { 2 } } = y$$

Solve for a

$$a\neq 0$$

$$y=\frac{\sqrt{3}}{12}\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Combine a and \frac{a}{2} to get \frac{3}{2}a.

$$\frac{\frac{a\sqrt{3}}{8}}{\frac{3}{2}a}=y$$

Express \frac{\frac{a\sqrt{3}}{8}}{\frac{3}{2}a} as a single fraction.

$$\frac{a\sqrt{3}}{8\times \frac{3}{2}a}=y$$

Multiply 8 and \frac{3}{2} to get 12.

$$\frac{a\sqrt{3}}{12a}=y$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12a.

$$a\sqrt{3}=y\times 12a$$

Reorder the terms.

$$\sqrt{3}a=12ay$$

Subtract 12ay from both sides.

$$\sqrt{3}a-12ay=0$$

Combine all terms containing a.

$$\left(\sqrt{3}-12y\right)a=0$$

The equation is in standard form.

$$\left(-12y+\sqrt{3}\right)a=0$$

Divide 0 by \sqrt{3}-12y.

$$a=0$$

Variable a cannot be equal to 0.

$$a\in \emptyset$$

Solve for y

$$y = \frac{\sqrt{3}}{12} = 0.14433756729740643$$

$$a\neq 0$$