Evaluate
\frac{\left(x-3\right)\left(x+4\right)\left(2x+1\right)}{2\left(x+2\right)\left(x^{2}+2x+2\right)}
Expand
\frac{2x^{3}+3x^{2}-23x-12}{2\left(x+2\right)\left(x^{2}+2x+2\right)}
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\frac{\left(2x^{2}-5x-3\right)\left(3x^{2}+11x-4\right)}{\left(3x^{2}+5x-2\right)\left(2x^{2}+4x+4\right)}
Divide \frac{2x^{2}-5x-3}{3x^{2}+5x-2} by \frac{2x^{2}+4x+4}{3x^{2}+11x-4} by multiplying \frac{2x^{2}-5x-3}{3x^{2}+5x-2} by the reciprocal of \frac{2x^{2}+4x+4}{3x^{2}+11x-4}.
\frac{\left(x-3\right)\left(3x-1\right)\left(x+4\right)\left(2x+1\right)}{2\left(3x-1\right)\left(x+2\right)\left(x^{2}+2x+2\right)}
Factor the expressions that are not already factored.
\frac{\left(x-3\right)\left(x+4\right)\left(2x+1\right)}{2\left(x+2\right)\left(x^{2}+2x+2\right)}
Cancel out 3x-1 in both numerator and denominator.
\frac{2x^{3}+3x^{2}-23x-12}{2x^{3}+8x^{2}+12x+8}
Expand the expression.
\frac{2\left(x-3\right)\left(\frac{1}{2}x+2\right)\left(2x+1\right)}{2\left(x+2\right)\left(x^{2}+2x+2\right)}
Factor the expressions that are not already factored.
\frac{\left(x-3\right)\left(\frac{1}{2}x+2\right)\left(2x+1\right)}{\left(x+2\right)\left(x^{2}+2x+2\right)}
Cancel out 2 in both numerator and denominator.
\frac{x^{3}+\frac{3}{2}x^{2}-\frac{23}{2}x-6}{x^{3}+4x^{2}+6x+4}
Expand the expression.
\frac{\left(2x^{2}-5x-3\right)\left(3x^{2}+11x-4\right)}{\left(3x^{2}+5x-2\right)\left(2x^{2}+4x+4\right)}
Divide \frac{2x^{2}-5x-3}{3x^{2}+5x-2} by \frac{2x^{2}+4x+4}{3x^{2}+11x-4} by multiplying \frac{2x^{2}-5x-3}{3x^{2}+5x-2} by the reciprocal of \frac{2x^{2}+4x+4}{3x^{2}+11x-4}.
\frac{\left(x-3\right)\left(3x-1\right)\left(x+4\right)\left(2x+1\right)}{2\left(3x-1\right)\left(x+2\right)\left(x^{2}+2x+2\right)}
Factor the expressions that are not already factored.
\frac{\left(x-3\right)\left(x+4\right)\left(2x+1\right)}{2\left(x+2\right)\left(x^{2}+2x+2\right)}
Cancel out 3x-1 in both numerator and denominator.
\frac{2x^{3}+3x^{2}-23x-12}{2x^{3}+8x^{2}+12x+8}
Expand the expression.
\frac{2\left(x-3\right)\left(\frac{1}{2}x+2\right)\left(2x+1\right)}{2\left(x+2\right)\left(x^{2}+2x+2\right)}
Factor the expressions that are not already factored.
\frac{\left(x-3\right)\left(\frac{1}{2}x+2\right)\left(2x+1\right)}{\left(x+2\right)\left(x^{2}+2x+2\right)}
Cancel out 2 in both numerator and denominator.
\frac{x^{3}+\frac{3}{2}x^{2}-\frac{23}{2}x-6}{x^{3}+4x^{2}+6x+4}
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}