Solve x^2-2x+1/x^2-9div3x+6/x^2+4x-4

$$\frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 9 } \div \frac { 3 x + 6 } { x ^ { 2 } + 4 x - 4 }$$

Evaluate

$$\frac{\left(x-1\right)^{2}\left(x^{2}+4x-4\right)}{3\left(x+2\right)\left(x^{2}-9\right)}$$

Short Solution Steps

Divide \frac{x^{2}-2x+1}{x^{2}-9} by \frac{3x+6}{x^{2}+4x-4} by multiplying \frac{x^{2}-2x+1}{x^{2}-9} by the reciprocal of \frac{3x+6}{x^{2}+4x-4}.

$$\frac{\left(x^{2}-2x+1\right)\left(x^{2}+4x-4\right)}{\left(x^{2}-9\right)\left(3x+6\right)}$$

Use the distributive property to multiply x^{2}-2x+1 by x^{2}+4x-4 and combine like terms.

$$\frac{x^{4}+2x^{3}-11x^{2}+12x-4}{\left(x^{2}-9\right)\left(3x+6\right)}$$

Use the distributive property to multiply x^{2}-9 by 3x+6.

$$\frac{x^{4}+2x^{3}-11x^{2}+12x-4}{3x^{3}+6x^{2}-27x-54}$$

Expand

$$\frac{x^{4}+2x^{3}-11x^{2}+12x-4}{3\left(x+2\right)\left(x^{2}-9\right)}$$

Short Solution Steps

Divide \frac{x^{2}-2x+1}{x^{2}-9} by \frac{3x+6}{x^{2}+4x-4} by multiplying \frac{x^{2}-2x+1}{x^{2}-9} by the reciprocal of \frac{3x+6}{x^{2}+4x-4}.

$$\frac{\left(x^{2}-2x+1\right)\left(x^{2}+4x-4\right)}{\left(x^{2}-9\right)\left(3x+6\right)}$$

Use the distributive property to multiply x^{2}-2x+1 by x^{2}+4x-4 and combine like terms.

$$\frac{x^{4}+2x^{3}-11x^{2}+12x-4}{\left(x^{2}-9\right)\left(3x+6\right)}$$

Use the distributive property to multiply x^{2}-9 by 3x+6.

$$\frac{x^{4}+2x^{3}-11x^{2}+12x-4}{3x^{3}+6x^{2}-27x-54}$$