Evaluate
\frac{a^{2}}{a^{2}-9}
Expand
\frac{a^{2}}{a^{2}-9}
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\frac{3a^{2}+6a}{\left(a-3\right)\left(a+3\right)}-\frac{2a}{a-3}
Factor a^{2}-9.
\frac{3a^{2}+6a}{\left(a-3\right)\left(a+3\right)}-\frac{2a\left(a+3\right)}{\left(a-3\right)\left(a+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(a-3\right)\left(a+3\right) and a-3 is \left(a-3\right)\left(a+3\right). Multiply \frac{2a}{a-3} times \frac{a+3}{a+3}.
\frac{3a^{2}+6a-2a\left(a+3\right)}{\left(a-3\right)\left(a+3\right)}
Since \frac{3a^{2}+6a}{\left(a-3\right)\left(a+3\right)} and \frac{2a\left(a+3\right)}{\left(a-3\right)\left(a+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3a^{2}+6a-2a^{2}-6a}{\left(a-3\right)\left(a+3\right)}
Do the multiplications in 3a^{2}+6a-2a\left(a+3\right).
\frac{a^{2}}{\left(a-3\right)\left(a+3\right)}
Combine like terms in 3a^{2}+6a-2a^{2}-6a.
\frac{a^{2}}{a^{2}-9}
Expand \left(a-3\right)\left(a+3\right).
\frac{3a^{2}+6a}{\left(a-3\right)\left(a+3\right)}-\frac{2a}{a-3}
Factor a^{2}-9.
\frac{3a^{2}+6a}{\left(a-3\right)\left(a+3\right)}-\frac{2a\left(a+3\right)}{\left(a-3\right)\left(a+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(a-3\right)\left(a+3\right) and a-3 is \left(a-3\right)\left(a+3\right). Multiply \frac{2a}{a-3} times \frac{a+3}{a+3}.
\frac{3a^{2}+6a-2a\left(a+3\right)}{\left(a-3\right)\left(a+3\right)}
Since \frac{3a^{2}+6a}{\left(a-3\right)\left(a+3\right)} and \frac{2a\left(a+3\right)}{\left(a-3\right)\left(a+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3a^{2}+6a-2a^{2}-6a}{\left(a-3\right)\left(a+3\right)}
Do the multiplications in 3a^{2}+6a-2a\left(a+3\right).
\frac{a^{2}}{\left(a-3\right)\left(a+3\right)}
Combine like terms in 3a^{2}+6a-2a^{2}-6a.
\frac{a^{2}}{a^{2}-9}
Expand \left(a-3\right)\left(a+3\right).
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699 * 533
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}