Evaluate
\frac{3\left(a-1\right)\left(a+2\right)}{2\left(a+b^{2}\right)}
Expand
\frac{3\left(a^{2}+a-2\right)}{2\left(a+b^{2}\right)}
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\frac{\frac{\left(a+1\right)\left(3a-3\right)}{\left(a-1\right)\left(2a+2\right)}}{\frac{b^{2}+a}{a^{2}+a-2}}
Multiply \frac{a+1}{a-1} times \frac{3a-3}{2a+2} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(a+1\right)\left(3a-3\right)\left(a^{2}+a-2\right)}{\left(a-1\right)\left(2a+2\right)\left(b^{2}+a\right)}
Divide \frac{\left(a+1\right)\left(3a-3\right)}{\left(a-1\right)\left(2a+2\right)} by \frac{b^{2}+a}{a^{2}+a-2} by multiplying \frac{\left(a+1\right)\left(3a-3\right)}{\left(a-1\right)\left(2a+2\right)} by the reciprocal of \frac{b^{2}+a}{a^{2}+a-2}.
\frac{3\left(a+1\right)\left(a+2\right)\left(a-1\right)^{2}}{2\left(a-1\right)\left(a+1\right)\left(a+b^{2}\right)}
Factor the expressions that are not already factored.
\frac{3\left(a-1\right)\left(a+2\right)}{2\left(a+b^{2}\right)}
Cancel out \left(a-1\right)\left(a+1\right) in both numerator and denominator.
\frac{3a^{2}+3a-6}{2a+2b^{2}}
Expand the expression.
\frac{\frac{\left(a+1\right)\left(3a-3\right)}{\left(a-1\right)\left(2a+2\right)}}{\frac{b^{2}+a}{a^{2}+a-2}}
Multiply \frac{a+1}{a-1} times \frac{3a-3}{2a+2} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(a+1\right)\left(3a-3\right)\left(a^{2}+a-2\right)}{\left(a-1\right)\left(2a+2\right)\left(b^{2}+a\right)}
Divide \frac{\left(a+1\right)\left(3a-3\right)}{\left(a-1\right)\left(2a+2\right)} by \frac{b^{2}+a}{a^{2}+a-2} by multiplying \frac{\left(a+1\right)\left(3a-3\right)}{\left(a-1\right)\left(2a+2\right)} by the reciprocal of \frac{b^{2}+a}{a^{2}+a-2}.
\frac{3\left(a+1\right)\left(a+2\right)\left(a-1\right)^{2}}{2\left(a-1\right)\left(a+1\right)\left(a+b^{2}\right)}
Factor the expressions that are not already factored.
\frac{3\left(a-1\right)\left(a+2\right)}{2\left(a+b^{2}\right)}
Cancel out \left(a-1\right)\left(a+1\right) in both numerator and denominator.
\frac{3a^{2}+3a-6}{2a+2b^{2}}
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}