Evaluate
-\frac{2x^{2}}{a\left(a-2\right)}
Expand
-\frac{2x^{2}}{a\left(a-2\right)}
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\frac{-2-a}{\left(a-2\right)\left(a^{2}+2a\right)}\times 6\times \frac{x^{2}}{3}
Multiply \frac{-2-a}{a-2} times \frac{1}{a^{2}+2a} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(-2-a\right)\times 6}{\left(a-2\right)\left(a^{2}+2a\right)}\times \frac{x^{2}}{3}
Express \frac{-2-a}{\left(a-2\right)\left(a^{2}+2a\right)}\times 6 as a single fraction.
\frac{\left(-2-a\right)\times 6x^{2}}{\left(a-2\right)\left(a^{2}+2a\right)\times 3}
Multiply \frac{\left(-2-a\right)\times 6}{\left(a-2\right)\left(a^{2}+2a\right)} times \frac{x^{2}}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{2\left(-a-2\right)x^{2}}{\left(a-2\right)\left(a^{2}+2a\right)}
Cancel out 3 in both numerator and denominator.
\frac{2\left(-a-2\right)x^{2}}{a\left(a-2\right)\left(a+2\right)}
Factor the expressions that are not already factored.
\frac{-2\left(a+2\right)x^{2}}{a\left(a-2\right)\left(a+2\right)}
Extract the negative sign in -2-a.
\frac{-2x^{2}}{a\left(a-2\right)}
Cancel out a+2 in both numerator and denominator.
\frac{-2x^{2}}{a^{2}-2a}
Expand the expression.
\frac{-2-a}{\left(a-2\right)\left(a^{2}+2a\right)}\times 6\times \frac{x^{2}}{3}
Multiply \frac{-2-a}{a-2} times \frac{1}{a^{2}+2a} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(-2-a\right)\times 6}{\left(a-2\right)\left(a^{2}+2a\right)}\times \frac{x^{2}}{3}
Express \frac{-2-a}{\left(a-2\right)\left(a^{2}+2a\right)}\times 6 as a single fraction.
\frac{\left(-2-a\right)\times 6x^{2}}{\left(a-2\right)\left(a^{2}+2a\right)\times 3}
Multiply \frac{\left(-2-a\right)\times 6}{\left(a-2\right)\left(a^{2}+2a\right)} times \frac{x^{2}}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{2\left(-a-2\right)x^{2}}{\left(a-2\right)\left(a^{2}+2a\right)}
Cancel out 3 in both numerator and denominator.
\frac{2\left(-a-2\right)x^{2}}{a\left(a-2\right)\left(a+2\right)}
Factor the expressions that are not already factored.
\frac{-2\left(a+2\right)x^{2}}{a\left(a-2\right)\left(a+2\right)}
Extract the negative sign in -2-a.
\frac{-2x^{2}}{a\left(a-2\right)}
Cancel out a+2 in both numerator and denominator.
\frac{-2x^{2}}{a^{2}-2a}
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}