Solve 3x^2-2x-1/x^2+6x+8div3x^2-13x+4/x^2+8x+16

$$\frac { 3 x ^ { 2 } - 2 x - 1 } { x ^ { 2 } + 6 x + 8 } \div \frac { 3 x ^ { 2 } - 13 x + 4 } { x ^ { 2 } + 8 x + 16 }$$

Evaluate

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

Short Solution Steps

Divide \frac{3x^{2}-2x-1}{x^{2}+6x+8} by \frac{3x^{2}-13x+4}{x^{2}+8x+16} by multiplying \frac{3x^{2}-2x-1}{x^{2}+6x+8} by the reciprocal of \frac{3x^{2}-13x+4}{x^{2}+8x+16}.

$$\frac{\left(3x^{2}-2x-1\right)\left(x^{2}+8x+16\right)}{\left(x^{2}+6x+8\right)\left(3x^{2}-13x+4\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x+4 in both numerator and denominator.

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

Expand the expression.

$$\frac{3x^{3}+10x^{2}-9x-4}{3x^{3}-7x^{2}-22x+8}$$

Expand

$$\frac{3x^{3}+10x^{2}-9x-4}{\left(x+2\right)\left(3x^{2}-13x+4\right)}$$

Short Solution Steps

Divide \frac{3x^{2}-2x-1}{x^{2}+6x+8} by \frac{3x^{2}-13x+4}{x^{2}+8x+16} by multiplying \frac{3x^{2}-2x-1}{x^{2}+6x+8} by the reciprocal of \frac{3x^{2}-13x+4}{x^{2}+8x+16}.

$$\frac{\left(3x^{2}-2x-1\right)\left(x^{2}+8x+16\right)}{\left(x^{2}+6x+8\right)\left(3x^{2}-13x+4\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x+4 in both numerator and denominator.

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

Expand the expression.

$$\frac{3x^{3}+10x^{2}-9x-4}{3x^{3}-7x^{2}-22x+8}$$