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\frac{\left(14+17x-6x^{2}\right)\left(2x^{2}+19x+42\right)}{\left(3x^{2}+20x+12\right)\left(4x^{2}-49\right)}
Divide \frac{14+17x-6x^{2}}{3x^{2}+20x+12} by \frac{4x^{2}-49}{2x^{2}+19x+42} by multiplying \frac{14+17x-6x^{2}}{3x^{2}+20x+12} by the reciprocal of \frac{4x^{2}-49}{2x^{2}+19x+42}.
\frac{\left(-3x-2\right)\left(2x-7\right)\left(x+6\right)\left(2x+7\right)}{\left(2x-7\right)\left(x+6\right)\left(2x+7\right)\left(3x+2\right)}
Factor the expressions that are not already factored.
\frac{-\left(2x-7\right)\left(x+6\right)\left(2x+7\right)\left(3x+2\right)}{\left(2x-7\right)\left(x+6\right)\left(2x+7\right)\left(3x+2\right)}
Extract the negative sign in -2-3x.
-1
Cancel out \left(2x-7\right)\left(x+6\right)\left(2x+7\right)\left(3x+2\right) in both numerator and denominator.
Examples
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\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
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