Solve ab/sqrt{2}=a

$$\frac { a b } { \sqrt { 2 } } = a$$

Solve for a

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&b=\sqrt{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{ab}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{ab\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=a$$

The square of \sqrt{2} is 2.

$$\frac{ab\sqrt{2}}{2}=a$$

Subtract a from both sides.

$$\frac{ab\sqrt{2}}{2}-a=0$$

Multiply both sides of the equation by 2.

$$ab\sqrt{2}-2a=0$$

Combine all terms containing a.

$$\left(b\sqrt{2}-2\right)a=0$$

The equation is in standard form.

$$\left(\sqrt{2}b-2\right)a=0$$

Divide 0 by b\sqrt{2}-2.

$$a=0$$

Solve for b

$$\left\{\begin{matrix}\\b=\sqrt{2}\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$