Solve aa3+9=abb

$$a a 3 + 9 = a b b$$

Solve for a

$$a=-\frac{9}{a_{3}-b^{2}}$$

$$a_{3}\neq b^{2}$$

Steps for Solving Linear Equation

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

$$aa_{3}+9=ab^{2}$$

Subtract ab^{2} from both sides.

$$aa_{3}+9-ab^{2}=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$aa_{3}-ab^{2}=-9$$

Combine all terms containing a.

$$\left(a_{3}-b^{2}\right)a=-9$$

Divide both sides by a_{3}-b^{2}.

$$\frac{\left(a_{3}-b^{2}\right)a}{a_{3}-b^{2}}=-\frac{9}{a_{3}-b^{2}}$$

Dividing by a_{3}-b^{2} undoes the multiplication by a_{3}-b^{2}.

$$a=-\frac{9}{a_{3}-b^{2}}$$

Solve for a_3

$$a_{3}=b^{2}-\frac{9}{a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

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

$$aa_{3}+9=ab^{2}$$

Subtract 9 from both sides.

$$aa_{3}=ab^{2}-9$$

Divide both sides by a.

$$\frac{aa_{3}}{a}=\frac{ab^{2}-9}{a}$$

Dividing by a undoes the multiplication by a.

$$a_{3}=\frac{ab^{2}-9}{a}$$

Divide ab^{2}-9 by a.

$$a_{3}=b^{2}-\frac{9}{a}$$