Evaluate
\frac{10+23x-6x^{2}}{\left(x-3\right)\left(x+2\right)}
Differentiate w.r.t. x
\frac{-17x^{2}+52x-128}{\left(\left(x-3\right)\left(x+2\right)\right)^{2}}
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\frac{5\left(x+2\right)}{\left(x-3\right)\left(x+2\right)}-\frac{6x\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and x+2 is \left(x-3\right)\left(x+2\right). Multiply \frac{5}{x-3} times \frac{x+2}{x+2}. Multiply \frac{6x}{x+2} times \frac{x-3}{x-3}.
\frac{5\left(x+2\right)-6x\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}
Since \frac{5\left(x+2\right)}{\left(x-3\right)\left(x+2\right)} and \frac{6x\left(x-3\right)}{\left(x-3\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{5x+10-6x^{2}+18x}{\left(x-3\right)\left(x+2\right)}
Do the multiplications in 5\left(x+2\right)-6x\left(x-3\right).
\frac{23x+10-6x^{2}}{\left(x-3\right)\left(x+2\right)}
Combine like terms in 5x+10-6x^{2}+18x.
\frac{23x+10-6x^{2}}{x^{2}-x-6}
Expand \left(x-3\right)\left(x+2\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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
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