Solve 3(2x^2-8x-1)/(x+4)(x+1)(2x-1)

$$\frac { 3 ( 2 x ^ { 2 } - 8 x - 1 ) } { ( x + 4 ) ( x + 1 ) ( 2 x - 1 ) }$$

Evaluate

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

Short Solution Steps

Use the distributive property to multiply 3 by 2x^{2}-8x-1.

$$\frac{6x^{2}-24x-3}{\left(x+4\right)\left(x+1\right)\left(2x-1\right)}$$

Use the distributive property to multiply x+4 by x+1 and combine like terms.

$$\frac{6x^{2}-24x-3}{\left(x^{2}+5x+4\right)\left(2x-1\right)}$$

Use the distributive property to multiply x^{2}+5x+4 by 2x-1 and combine like terms.

$$\frac{6x^{2}-24x-3}{2x^{3}+9x^{2}+3x-4}$$

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

$$\frac{3x^{2}-12x-\frac{3}{2}}{x^{3}+\frac{9}{2}x^{2}+\frac{3}{2}x-2}$$

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

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

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

$$\frac{\frac{3}{4}x^{2}-3x-\frac{3}{8}}{\frac{1}{4}x^{3}+\frac{9}{8}x^{2}+\frac{3}{8}x-\frac{1}{2}}$$

Expand

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

Short Solution Steps

Use the distributive property to multiply 3 by 2x^{2}-8x-1.

$$\frac{6x^{2}-24x-3}{\left(x+4\right)\left(x+1\right)\left(2x-1\right)}$$

Use the distributive property to multiply x+4 by x+1 and combine like terms.

$$\frac{6x^{2}-24x-3}{\left(x^{2}+5x+4\right)\left(2x-1\right)}$$

Use the distributive property to multiply x^{2}+5x+4 by 2x-1 and combine like terms.

$$\frac{6x^{2}-24x-3}{2x^{3}+9x^{2}+3x-4}$$

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

$$\frac{3x^{2}-12x-\frac{3}{2}}{x^{3}+\frac{9}{2}x^{2}+\frac{3}{2}x-2}$$

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

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

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

$$\frac{\frac{3}{4}x^{2}-3x-\frac{3}{8}}{\frac{1}{4}x^{3}+\frac{9}{8}x^{2}+\frac{3}{8}x-\frac{1}{2}}$$