Evaluate
\frac{8x^{2}-60x-43}{\left(3x-2\right)\left(2x+3\right)\left(4x+1\right)}
Expand
\frac{8x^{2}-60x-43}{\left(3x-2\right)\left(2x+3\right)\left(4x+1\right)}
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\frac{8x^{2}-60x-43}{\left(8x^{2}+14x+3\right)\left(3x-2\right)}
Use the distributive property to multiply 4x+1 by 2x+3 and combine like terms.
\frac{8x^{2}-60x-43}{24x^{3}+26x^{2}-19x-6}
Use the distributive property to multiply 8x^{2}+14x+3 by 3x-2 and combine like terms.
\frac{8\left(x-\left(-\frac{1}{4}\sqrt{311}+\frac{15}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{311}+\frac{15}{4}\right)\right)}{6\left(\frac{1}{2}x-\frac{1}{3}\right)\left(2x+3\right)\left(4x+1\right)}
Factor the expressions that are not already factored.
\frac{4\left(x-\left(-\frac{1}{4}\sqrt{311}+\frac{15}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{311}+\frac{15}{4}\right)\right)}{3\left(\frac{1}{2}x-\frac{1}{3}\right)\left(2x+3\right)\left(4x+1\right)}
Cancel out 2 in both numerator and denominator.
\frac{4x^{2}-30x-\frac{43}{2}}{12x^{3}+13x^{2}-\frac{19}{2}x-3}
Expand the expression.
\frac{8x^{2}-60x-43}{\left(8x^{2}+14x+3\right)\left(3x-2\right)}
Use the distributive property to multiply 4x+1 by 2x+3 and combine like terms.
\frac{8x^{2}-60x-43}{24x^{3}+26x^{2}-19x-6}
Use the distributive property to multiply 8x^{2}+14x+3 by 3x-2 and combine like terms.
\frac{8\left(x-\left(-\frac{1}{4}\sqrt{311}+\frac{15}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{311}+\frac{15}{4}\right)\right)}{6\left(\frac{1}{2}x-\frac{1}{3}\right)\left(2x+3\right)\left(4x+1\right)}
Factor the expressions that are not already factored.
\frac{4\left(x-\left(-\frac{1}{4}\sqrt{311}+\frac{15}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{311}+\frac{15}{4}\right)\right)}{3\left(\frac{1}{2}x-\frac{1}{3}\right)\left(2x+3\right)\left(4x+1\right)}
Cancel out 2 in both numerator and denominator.
\frac{4x^{2}-30x-\frac{43}{2}}{12x^{3}+13x^{2}-\frac{19}{2}x-3}
Expand the expression.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}