Solve {l}{6a^2+4a-11}{9a^2-6a-4}

$$\left. \begin{array} { l } { 6 a ^ { 2 } + 4 a - 11 } \\ { 9 a ^ { 2 } - 6 a - 4 } \end{array} \right.$$

Least Common Multiple

$$\frac{\left(\left(3a-1\right)^{2}-5\right)\left(\left(6a+2\right)^{2}-70\right)}{6}$$

Solution Steps

Factor the expressions that are not already factored.

$$6a^{2}+4a-11=6\left(a-\left(-\frac{1}{6}\sqrt{70}-\frac{1}{3}\right)\right)\left(a-\left(\frac{1}{6}\sqrt{70}-\frac{1}{3}\right)\right) 9a^{2}-6a-4=9\left(a-\left(-\frac{1}{3}\sqrt{5}+\frac{1}{3}\right)\right)\left(a-\left(\frac{1}{3}\sqrt{5}+\frac{1}{3}\right)\right)$$

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

$$54\left(a-\frac{1-\sqrt{5}}{3}\right)\left(a-\left(-\frac{\sqrt{70}}{6}-\frac{1}{3}\right)\right)\left(a-\frac{\sqrt{5}+1}{3}\right)\left(a-\left(\frac{\sqrt{70}}{6}-\frac{1}{3}\right)\right)$$

Expand the expression.

$$54a^{4}-147a^{2}+50a+44$$

Evaluate

$$6a^{2}+4a-11,\ 9a^{2}-6a-4$$