Solve frac{x^{3}+2x^2-3}{(x-1)^2(x+2)(x^2+x+1)^2}

$$\frac { x ^ { 3 } + 2 x ^ { 2 } - 3 } { ( x - 1 ) ^ { 2 } ( x + 2 ) ( x ^ { 2 } + x + 1 ) ^ { 2 } }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{2}+3x+3}{x^{6}+3x^{5}+3x^{4}+x^{3}-3x^{2}-3x-2}$$

Expand

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{2}+3x+3}{x^{6}+3x^{5}+3x^{4}+x^{3}-3x^{2}-3x-2}$$