Evaluate
\frac{a^{7}-1}{a\left(a^{2}-1\right)^{2}}
Expand
\frac{a^{7}-1}{a^{5}-2a^{3}+a}
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\frac{\left(a-1\right)\left(a^{6}+a^{5}+a^{4}+a^{3}+a^{2}+a+1\right)}{a\left(a-1\right)^{2}\left(a+1\right)^{2}}
Factor the expressions that are not already factored.
\frac{a^{6}+a^{5}+a^{4}+a^{3}+a^{2}+a+1}{a\left(a-1\right)\left(a+1\right)^{2}}
Cancel out a-1 in both numerator and denominator.
\frac{a^{6}+a^{5}+a^{4}+a^{3}+a^{2}+a+1}{a^{4}+a^{3}-a^{2}-a}
Expand the expression.
\frac{\left(a-1\right)\left(a^{6}+a^{5}+a^{4}+a^{3}+a^{2}+a+1\right)}{a\left(a-1\right)^{2}\left(a+1\right)^{2}}
Factor the expressions that are not already factored.
\frac{a^{6}+a^{5}+a^{4}+a^{3}+a^{2}+a+1}{a\left(a-1\right)\left(a+1\right)^{2}}
Cancel out a-1 in both numerator and denominator.
\frac{a^{6}+a^{5}+a^{4}+a^{3}+a^{2}+a+1}{a^{4}+a^{3}-a^{2}-a}
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}