Solve {l}{2x^2-25x+12}{(4x-6)3x-1}

$$\left. \begin{array} { l } { 2 x ^ { 2 } - 25 x + 12 } \\ { ( 4 x - 6 ) 3 x - 1 } \end{array} \right.$$

Least Common Multiple

$$\left(x-12\right)\left(2x-1\right)\left(12x^{2}-18x-1\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$2x^{2}-25x+12=\left(x-12\right)\left(2x-1\right) 6\left(2x-3\right)x-1=12\left(x-\left(-\frac{1}{12}\sqrt{93}+\frac{3}{4}\right)\right)\left(x-\left(\frac{1}{12}\sqrt{93}+\frac{3}{4}\right)\right)$$

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

$$12\left(x-12\right)\left(2x-1\right)\left(x-\left(-\frac{\sqrt{93}}{12}+\frac{3}{4}\right)\right)\left(x-\left(\frac{\sqrt{93}}{12}+\frac{3}{4}\right)\right)$$

Expand the expression.

$$24x^{4}-336x^{3}+592x^{2}-191x-12$$

Evaluate

$$2x^{2}-25x+12,\ 6x\left(2x-3\right)-1$$