Solve frac{20a^{2}b}{4a^2bc-8a^2b}=36a^2/9a^2-36a=

$$\frac { 20 a ^ { 2 } b } { 4 a ^ { 2 } b c - 8 a ^ { 2 } b } = \frac { 36 a ^ { 2 } } { 9 a ^ { 2 } - 36 a } =$$

Solve for b

$$b\neq 0$$

$$a=\frac{20}{13-4c}\text{ and }c\neq \frac{13}{4}\text{ and }c\neq 2$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 36b\left(a-4\right)\left(c-2\right)a^{2}, the least common multiple of 4a^{2}bc-8a^{2}b,9a^{2}-36a.

$$\left(9a-36\right)\times 20a^{2}b=4b\left(c-2\right)a\times 36a^{2}$$

Use the distributive property to multiply 9a-36 by 20.

$$\left(180a-720\right)a^{2}b=4b\left(c-2\right)a\times 36a^{2}$$

Use the distributive property to multiply 180a-720 by a^{2}.

$$\left(180a^{3}-720a^{2}\right)b=4b\left(c-2\right)a\times 36a^{2}$$

Use the distributive property to multiply 180a^{3}-720a^{2} by b.

$$180a^{3}b-720a^{2}b=4b\left(c-2\right)a\times 36a^{2}$$

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

$$180a^{3}b-720a^{2}b=4b\left(c-2\right)a^{3}\times 36$$

Multiply 4 and 36 to get 144.

$$180a^{3}b-720a^{2}b=144b\left(c-2\right)a^{3}$$

Use the distributive property to multiply 144b by c-2.

$$180a^{3}b-720a^{2}b=\left(144bc-288b\right)a^{3}$$

Use the distributive property to multiply 144bc-288b by a^{3}.

$$180a^{3}b-720a^{2}b=144bca^{3}-288ba^{3}$$

Subtract 144bca^{3} from both sides.

$$180a^{3}b-720a^{2}b-144bca^{3}=-288ba^{3}$$

Add 288ba^{3} to both sides.

$$180a^{3}b-720a^{2}b-144bca^{3}+288ba^{3}=0$$

Combine 180a^{3}b and 288ba^{3} to get 468a^{3}b.

$$468a^{3}b-720a^{2}b-144bca^{3}=0$$

Combine all terms containing b.

$$\left(468a^{3}-720a^{2}-144ca^{3}\right)b=0$$

Divide 0 by 468a^{3}-720a^{2}-144ca^{3}.

$$b=0$$

Variable b cannot be equal to 0.

$$b\in \emptyset$$

Solve for a

$$a=\frac{20}{13-4c}$$

$$c\neq 2\text{ and }c\neq \frac{13}{4}\text{ and }b\neq 0$$