Solve c/y+b/a=c/b

$$\frac { c } { y } + \frac { b } { a } = \frac { c } { b }$$

Solve for a

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

$$b\neq 0\text{ and }y\neq 0\text{ and }y\neq b\text{ and }c\neq 0$$

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 aby, the least common multiple of y,a,b.

$$abc+byb=ayc$$

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

$$abc+b^{2}y=ayc$$

Subtract ayc from both sides.

$$abc+b^{2}y-ayc=0$$

Subtract b^{2}y from both sides. Anything subtracted from zero gives its negation.

$$abc-ayc=-b^{2}y$$

Combine all terms containing a.

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

The equation is in standard form.

$$\left(bc-cy\right)a=-yb^{2}$$

Divide both sides by -cy+bc.

$$\frac{\left(bc-cy\right)a}{bc-cy}=-\frac{yb^{2}}{bc-cy}$$

Dividing by -cy+bc undoes the multiplication by -cy+bc.

$$a=-\frac{yb^{2}}{bc-cy}$$

Divide -b^{2}y by -cy+bc.

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

Variable a cannot be equal to 0.

$$a=-\frac{yb^{2}}{c\left(b-y\right)}\text{, }a\neq 0$$

Solve for b (complex solution)

$$b=\frac{\sqrt{ac\left(4y^{2}+ac\right)}-ac}{2y}$$

$$b=-\frac{\sqrt{ac\left(4y^{2}+ac\right)}+ac}{2y}\text{, }y\neq 0\text{ and }a\neq 0\text{ and }c\neq 0$$