Solve {l}{frac{6x^{4}-8x^{2}-x^{3}+x+2}{2x^{2}-x-1}}{frac{3x^{4}+2x^{3}+3x-6x^{2}-2}{x^{2}+x-2}}{4x^4-4x^3-13x^2+11x+4/2x^2-4+x}

$$\left. \begin{array} { l } { \frac { 6 x ^ { 4 } - 8 x ^ { 2 } - x ^ { 3 } + x + 2 } { 2 x ^ { 2 } - x - 1 } } \\ { \frac { 3 x ^ { 4 } + 2 x ^ { 3 } + 3 x - 6 x ^ { 2 } - 2 } { x ^ { 2 } + x - 2 } } \\ { \frac { 4 x ^ { 4 } - 4 x ^ { 3 } - 13 x ^ { 2 } + 11 x + 4 } { 2 x ^ { 2 } - 4 + x } } \end{array} \right.$$

Least Common Multiple

$$\left(3x-2\right)\left(x+1\right)\left(6x^{4}-11x^{3}+2x^{2}-2x-1\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$-2+x+3x^{2}=\left(3x-2\right)\left(x+1\right) -1-3x+2x^{2}=2\left(x-\left(-\frac{1}{4}\sqrt{17}+\frac{3}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{17}+\frac{3}{4}\right)\right)$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$\left(3x-2\right)\left(x+1\right)\left(6x^{4}-11x^{3}+2x^{2}-2x-1\right)$$

Expand the expression.

$$18x^{6}-27x^{5}-17x^{4}+18x^{3}-9x^{2}+3x+2$$

Evaluate

$$3x^{2}+x-2,\ 3x^{2}-x+1,\ 2x^{2}-3x-1$$