Solve ay/b^2-y/b=a-b

$$\frac { a y } { b ^ { 2 } } - \frac { y } { b } = a - b$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=b\text{, }&b\neq 0\\a\in \mathrm{C}\text{, }&y=b^{2}\text{ and }b\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by b^{2}, the least common multiple of b^{2},b.

$$ay-by=b^{2}a-bb^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$ay-by=b^{2}a-b^{3}$$

Subtract b^{2}a from both sides.

$$ay-by-b^{2}a=-b^{3}$$

Add by to both sides.

$$ay-b^{2}a=-b^{3}+by$$

Combine all terms containing a.

$$\left(y-b^{2}\right)a=-b^{3}+by$$

The equation is in standard form.

$$\left(y-b^{2}\right)a=by-b^{3}$$

Divide both sides by y-b^{2}.

$$\frac{\left(y-b^{2}\right)a}{y-b^{2}}=\frac{b\left(y-b^{2}\right)}{y-b^{2}}$$

Dividing by y-b^{2} undoes the multiplication by y-b^{2}.

$$a=\frac{b\left(y-b^{2}\right)}{y-b^{2}}$$

Divide b\left(-b^{2}+y\right) by y-b^{2}.

$$a=b$$

Solve for a

$$\left\{\begin{matrix}a=b\text{, }&b\neq 0\\a\in \mathrm{R}\text{, }&y=b^{2}\text{ and }b\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by b^{2}, the least common multiple of b^{2},b.

$$ay-by=b^{2}a-bb^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$ay-by=b^{2}a-b^{3}$$

Subtract b^{2}a from both sides.

$$ay-by-b^{2}a=-b^{3}$$

Add by to both sides.

$$ay-b^{2}a=-b^{3}+by$$

Combine all terms containing a.

$$\left(y-b^{2}\right)a=-b^{3}+by$$

The equation is in standard form.

$$\left(y-b^{2}\right)a=by-b^{3}$$

Divide both sides by y-b^{2}.

$$\frac{\left(y-b^{2}\right)a}{y-b^{2}}=\frac{b\left(y-b^{2}\right)}{y-b^{2}}$$

Dividing by y-b^{2} undoes the multiplication by y-b^{2}.

$$a=\frac{b\left(y-b^{2}\right)}{y-b^{2}}$$

Divide b\left(-b^{2}+y\right) by y-b^{2}.

$$a=b$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\sqrt{y}\text{; }b=\sqrt{y}\text{, }&y\neq 0\\b=a\text{, }&a\neq 0\end{matrix}\right.$$

Solve for b

$$\left\{\begin{matrix}b=\sqrt{y}\text{; }b=-\sqrt{y}\text{, }&y>0\\b=a\text{, }&a\neq 0\end{matrix}\right.$$