Evaluate
\frac{a^{2}-2}{\left(a-1\right)^{2}}
Expand
\frac{a^{2}-2}{a^{2}-2a+1}
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\frac{\frac{2}{a+2}+\frac{\left(a-2\right)\left(a+2\right)}{a+2}}{\frac{a^{2}-2a+1}{a+2}}
To add or subtract expressions, expand them to make their denominators the same. Multiply a-2 times \frac{a+2}{a+2}.
\frac{\frac{2+\left(a-2\right)\left(a+2\right)}{a+2}}{\frac{a^{2}-2a+1}{a+2}}
Since \frac{2}{a+2} and \frac{\left(a-2\right)\left(a+2\right)}{a+2} have the same denominator, add them by adding their numerators.
\frac{\frac{2+a^{2}+2a-2a-4}{a+2}}{\frac{a^{2}-2a+1}{a+2}}
Do the multiplications in 2+\left(a-2\right)\left(a+2\right).
\frac{\frac{-2+a^{2}}{a+2}}{\frac{a^{2}-2a+1}{a+2}}
Combine like terms in 2+a^{2}+2a-2a-4.
\frac{\left(-2+a^{2}\right)\left(a+2\right)}{\left(a+2\right)\left(a^{2}-2a+1\right)}
Divide \frac{-2+a^{2}}{a+2} by \frac{a^{2}-2a+1}{a+2} by multiplying \frac{-2+a^{2}}{a+2} by the reciprocal of \frac{a^{2}-2a+1}{a+2}.
\frac{a^{2}-2}{a^{2}-2a+1}
Cancel out a+2 in both numerator and denominator.
\frac{\frac{2}{a+2}+\frac{\left(a-2\right)\left(a+2\right)}{a+2}}{\frac{a^{2}-2a+1}{a+2}}
To add or subtract expressions, expand them to make their denominators the same. Multiply a-2 times \frac{a+2}{a+2}.
\frac{\frac{2+\left(a-2\right)\left(a+2\right)}{a+2}}{\frac{a^{2}-2a+1}{a+2}}
Since \frac{2}{a+2} and \frac{\left(a-2\right)\left(a+2\right)}{a+2} have the same denominator, add them by adding their numerators.
\frac{\frac{2+a^{2}+2a-2a-4}{a+2}}{\frac{a^{2}-2a+1}{a+2}}
Do the multiplications in 2+\left(a-2\right)\left(a+2\right).
\frac{\frac{-2+a^{2}}{a+2}}{\frac{a^{2}-2a+1}{a+2}}
Combine like terms in 2+a^{2}+2a-2a-4.
\frac{\left(-2+a^{2}\right)\left(a+2\right)}{\left(a+2\right)\left(a^{2}-2a+1\right)}
Divide \frac{-2+a^{2}}{a+2} by \frac{a^{2}-2a+1}{a+2} by multiplying \frac{-2+a^{2}}{a+2} by the reciprocal of \frac{a^{2}-2a+1}{a+2}.
\frac{a^{2}-2}{a^{2}-2a+1}
Cancel out a+2 in both numerator and denominator.
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}