Solve {l}{(-8x^{3}+8x^{5}-5+2x^{4})-(-6-7x^{4}+4x^{5}-6x^{3})}{2(-2x^{4}+9x^3-3x)-3(8x^4-9x^3+6x^2-2x)}

$$\left. \begin{array} { l } { ( - 8 x ^ { 3 } + 8 x ^ { 5 } - 5 + 2 x ^ { 4 } ) - ( - 6 - 7 x ^ { 4 } + 4 x ^ { 5 } - 6 x ^ { 3 } ) } \\ { 2 ( - 2 x ^ { 4 } + 9 x ^ { 3 } - 3 x ) - 3 ( 8 x ^ { 4 } - 9 x ^ { 3 } + 6 x ^ { 2 } - 2 x ) } \end{array} \right.$$

Least Common Multiple

$$\left(4x-3\right)\left(7x-6\right)x^{2}\left(4x^{5}+9x^{4}-2x^{3}+1\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$-18x^{2}+45x^{3}-28x^{4}=\left(4x-3\right)\left(-7x+6\right)x^{2}$$

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

$$\left(4x-3\right)\left(7x-6\right)x^{2}\left(4x^{5}+9x^{4}-2x^{3}+1\right)$$

Expand the expression.

$$112x^{9}+72x^{8}-389x^{7}+252x^{6}-36x^{5}+28x^{4}-45x^{3}+18x^{2}$$

Evaluate

$$4x^{5}+9x^{4}-2x^{3}+1,\ \left(6-7x\right)\left(4x-3\right)x^{2}$$