Solve a^2+b^2/ab=a+c/b

$$\frac { a ^ { 2 } + b ^ { 2 } } { a b } = \frac { a + c } { b }$$

Solve for a

$$a=\frac{b^{2}}{c}$$

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

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 ab, the least common multiple of ab,b.

$$a^{2}+b^{2}=a\left(a+c\right)$$

Use the distributive property to multiply a by a+c.

$$a^{2}+b^{2}=a^{2}+ac$$

Subtract a^{2} from both sides.

$$a^{2}+b^{2}-a^{2}=ac$$

Combine a^{2} and -a^{2} to get 0.

$$b^{2}=ac$$

Swap sides so that all variable terms are on the left hand side.

$$ac=b^{2}$$

The equation is in standard form.

$$ca=b^{2}$$

Divide both sides by c.

$$\frac{ca}{c}=\frac{b^{2}}{c}$$

Dividing by c undoes the multiplication by c.

$$a=\frac{b^{2}}{c}$$

Variable a cannot be equal to 0.

$$a=\frac{b^{2}}{c}\text{, }a\neq 0$$

Solve for b (complex solution)

$$b=-\sqrt{a}\sqrt{c}$$

$$b=\sqrt{a}\sqrt{c}\text{, }a\neq 0\text{ and }c\neq 0$$

Solve for b

$$b=\sqrt{ac}$$

$$b=-\sqrt{ac}\text{, }\left(c<0\text{ and }a<0\right)\text{ or }\left(a>0\text{ and }c>0\right)$$