Solve 6x^2-40x-14/(5x-2)(2x-3)(x+4

$$\frac { 6 x ^ { 2 } - 40 x - 14 } { ( 5 x - 2 ) ( 2 x - 3 ) ( x + 4 }$$

Evaluate

$$\frac{2\left(x-7\right)\left(3x+1\right)}{\left(2x-3\right)\left(5x-2\right)\left(x+4\right)}$$

Short Solution Steps

Use the distributive property to multiply 5x-2 by 2x-3 and combine like terms.

$$\frac{6x^{2}-40x-14}{\left(10x^{2}-19x+6\right)\left(x+4\right)}$$

Use the distributive property to multiply 10x^{2}-19x+6 by x+4 and combine like terms.

$$\frac{6x^{2}-40x-14}{10x^{3}+21x^{2}-70x+24}$$

Factor the expressions that are not already factored.

$$\frac{2\left(x-7\right)\left(3x+1\right)}{2\left(2x-3\right)\left(5x-2\right)\left(\frac{1}{2}x+2\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\left(x-7\right)\left(3x+1\right)}{\left(2x-3\right)\left(5x-2\right)\left(\frac{1}{2}x+2\right)}$$

Expand the expression.

$$\frac{3x^{2}-20x-7}{5x^{3}+\frac{21}{2}x^{2}-35x+12}$$

Expand

$$\frac{2\left(3x^{2}-20x-7\right)}{\left(2x-3\right)\left(5x-2\right)\left(x+4\right)}$$

Short Solution Steps

Use the distributive property to multiply 5x-2 by 2x-3 and combine like terms.

$$\frac{6x^{2}-40x-14}{\left(10x^{2}-19x+6\right)\left(x+4\right)}$$

Use the distributive property to multiply 10x^{2}-19x+6 by x+4 and combine like terms.

$$\frac{6x^{2}-40x-14}{10x^{3}+21x^{2}-70x+24}$$

Factor the expressions that are not already factored.

$$\frac{2\left(x-7\right)\left(3x+1\right)}{2\left(2x-3\right)\left(5x-2\right)\left(\frac{1}{2}x+2\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\left(x-7\right)\left(3x+1\right)}{\left(2x-3\right)\left(5x-2\right)\left(\frac{1}{2}x+2\right)}$$

Expand the expression.

$$\frac{3x^{2}-20x-7}{5x^{3}+\frac{21}{2}x^{2}-35x+12}$$