Evaluate
\frac{\pi \left(a^{2}-9a+2\right)}{\left(2a+1\right)\left(a-1\right)^{2}}
Expand
\frac{\pi a^{2}-9\pi a+2\pi }{\left(2a+1\right)\left(a^{2}-2a+1\right)}
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\frac{\pi \left(2a-1\right)}{a^{2}-2a+1}\times \frac{a^{2}-9a+2}{4a^{2}-1}
Express \pi \times \frac{2a-1}{a^{2}-2a+1} as a single fraction.
\frac{\pi \left(2a-1\right)\left(a^{2}-9a+2\right)}{\left(a^{2}-2a+1\right)\left(4a^{2}-1\right)}
Multiply \frac{\pi \left(2a-1\right)}{a^{2}-2a+1} times \frac{a^{2}-9a+2}{4a^{2}-1} by multiplying numerator times numerator and denominator times denominator.
\frac{\pi \left(2a-1\right)\left(a-\left(-\frac{1}{2}\sqrt{73}+\frac{9}{2}\right)\right)\left(a-\left(\frac{1}{2}\sqrt{73}+\frac{9}{2}\right)\right)}{\left(2a-1\right)\left(2a+1\right)\left(a-1\right)^{2}}
Factor the expressions that are not already factored.
\frac{\pi \left(a-\left(-\frac{1}{2}\sqrt{73}+\frac{9}{2}\right)\right)\left(a-\left(\frac{1}{2}\sqrt{73}+\frac{9}{2}\right)\right)}{\left(2a+1\right)\left(a-1\right)^{2}}
Cancel out 2a-1 in both numerator and denominator.
\frac{\pi a^{2}-9\pi a+2\pi }{2a^{3}-3a^{2}+1}
Expand the expression.
\frac{\pi \left(2a-1\right)}{a^{2}-2a+1}\times \frac{a^{2}-9a+2}{4a^{2}-1}
Express \pi \times \frac{2a-1}{a^{2}-2a+1} as a single fraction.
\frac{\pi \left(2a-1\right)\left(a^{2}-9a+2\right)}{\left(a^{2}-2a+1\right)\left(4a^{2}-1\right)}
Multiply \frac{\pi \left(2a-1\right)}{a^{2}-2a+1} times \frac{a^{2}-9a+2}{4a^{2}-1} by multiplying numerator times numerator and denominator times denominator.
\frac{\pi \left(2a-1\right)\left(a-\left(-\frac{1}{2}\sqrt{73}+\frac{9}{2}\right)\right)\left(a-\left(\frac{1}{2}\sqrt{73}+\frac{9}{2}\right)\right)}{\left(2a-1\right)\left(2a+1\right)\left(a-1\right)^{2}}
Factor the expressions that are not already factored.
\frac{\pi \left(a-\left(-\frac{1}{2}\sqrt{73}+\frac{9}{2}\right)\right)\left(a-\left(\frac{1}{2}\sqrt{73}+\frac{9}{2}\right)\right)}{\left(2a+1\right)\left(a-1\right)^{2}}
Cancel out 2a-1 in both numerator and denominator.
\frac{\pi a^{2}-9\pi a+2\pi }{2a^{3}-3a^{2}+1}
Expand the expression.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}