Solve A=(x^2-4)(x^2-4x+3)/3(1-x)(x^2-x-6)=

$$A = \frac { ( x ^ { 2 } - 4 ) ( x ^ { 2 } - 4 x + 3 ) } { 3 ( 1 - x ) ( x ^ { 2 } - x - 6 ) } =$$

Solve for A (complex solution)

$$A=\frac{2-x}{3}$$

$$x\neq -2\text{ and }x\neq 3\text{ and }x\neq 1$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(x^{2}-4\right)\left(x^{2}-4x+3\right)}{3\left(1-x\right)\left(x^{2}-x-6\right)}.

$$A=\frac{\left(x-3\right)\left(x-2\right)\left(x-1\right)\left(x+2\right)}{3\left(x-3\right)\left(x+2\right)\left(-x+1\right)}$$

Extract the negative sign in -1+x.

$$A=\frac{-\left(x-3\right)\left(x-2\right)\left(x+2\right)\left(-x+1\right)}{3\left(x-3\right)\left(x+2\right)\left(-x+1\right)}$$

Cancel out \left(x-3\right)\left(x+2\right)\left(-x+1\right) in both numerator and denominator.

$$A=\frac{-\left(x-2\right)}{3}$$

To find the opposite of x-2, find the opposite of each term.

$$A=\frac{-x+2}{3}$$

Divide each term of -x+2 by 3 to get -\frac{1}{3}x+\frac{2}{3}.

$$A=-\frac{1}{3}x+\frac{2}{3}$$

Solve for A

$$A=\frac{2-x}{3}$$

$$x\neq 3\text{ and }x\neq -2\text{ and }x\neq 1$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(x^{2}-4\right)\left(x^{2}-4x+3\right)}{3\left(1-x\right)\left(x^{2}-x-6\right)}.

$$A=\frac{\left(x-3\right)\left(x-2\right)\left(x-1\right)\left(x+2\right)}{3\left(x-3\right)\left(x+2\right)\left(-x+1\right)}$$

Extract the negative sign in -1+x.

$$A=\frac{-\left(x-3\right)\left(x-2\right)\left(x+2\right)\left(-x+1\right)}{3\left(x-3\right)\left(x+2\right)\left(-x+1\right)}$$

Cancel out \left(x-3\right)\left(x+2\right)\left(-x+1\right) in both numerator and denominator.

$$A=\frac{-\left(x-2\right)}{3}$$

To find the opposite of x-2, find the opposite of each term.

$$A=\frac{-x+2}{3}$$

Divide each term of -x+2 by 3 to get -\frac{1}{3}x+\frac{2}{3}.

$$A=-\frac{1}{3}x+\frac{2}{3}$$

Solve for x (complex solution)

$$x=2-3A$$

$$A\neq \frac{4}{3}\text{ and }A\neq -\frac{1}{3}\text{ and }A\neq \frac{1}{3}$$

Solve for x

$$x=2-3A$$

$$A\neq \frac{4}{3}\text{ and }|A|\neq \frac{1}{3}$$