Evaluate
\frac{17a+4}{2\left(a+2\right)\left(a^{2}-1\right)\left(a^{2}+4\right)}
Expand
\frac{17a+4}{2\left(a^{2}-1\right)\left(a^{3}+2a^{2}+4a+8\right)}
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\frac{\frac{5a+12a+4}{a^{4}-16}}{\frac{2a^{3}-2a}{a^{2}-2a}}
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
\frac{\left(5a+12a+4\right)\left(a^{2}-2a\right)}{\left(a^{4}-16\right)\left(2a^{3}-2a\right)}
Divide \frac{5a+12a+4}{a^{4}-16} by \frac{2a^{3}-2a}{a^{2}-2a} by multiplying \frac{5a+12a+4}{a^{4}-16} by the reciprocal of \frac{2a^{3}-2a}{a^{2}-2a}.
\frac{\left(17a+4\right)\left(a^{2}-2a\right)}{\left(a^{4}-16\right)\left(2a^{3}-2a\right)}
Combine 5a and 12a to get 17a.
\frac{a\left(a-2\right)\left(17a+4\right)}{2a\left(a-2\right)\left(a-1\right)\left(a+1\right)\left(a+2\right)\left(a^{2}+4\right)}
Factor the expressions that are not already factored.
\frac{17a+4}{2\left(a-1\right)\left(a+1\right)\left(a+2\right)\left(a^{2}+4\right)}
Cancel out a\left(a-2\right) in both numerator and denominator.
\frac{17a+4}{2a^{5}+4a^{4}+6a^{3}+12a^{2}-8a-16}
Expand the expression.
\frac{\frac{5a+12a+4}{a^{4}-16}}{\frac{2a^{3}-2a}{a^{2}-2a}}
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
\frac{\left(5a+12a+4\right)\left(a^{2}-2a\right)}{\left(a^{4}-16\right)\left(2a^{3}-2a\right)}
Divide \frac{5a+12a+4}{a^{4}-16} by \frac{2a^{3}-2a}{a^{2}-2a} by multiplying \frac{5a+12a+4}{a^{4}-16} by the reciprocal of \frac{2a^{3}-2a}{a^{2}-2a}.
\frac{\left(17a+4\right)\left(a^{2}-2a\right)}{\left(a^{4}-16\right)\left(2a^{3}-2a\right)}
Combine 5a and 12a to get 17a.
\frac{a\left(a-2\right)\left(17a+4\right)}{2a\left(a-2\right)\left(a-1\right)\left(a+1\right)\left(a+2\right)\left(a^{2}+4\right)}
Factor the expressions that are not already factored.
\frac{17a+4}{2\left(a-1\right)\left(a+1\right)\left(a+2\right)\left(a^{2}+4\right)}
Cancel out a\left(a-2\right) in both numerator and denominator.
\frac{17a+4}{2a^{5}+4a^{4}+6a^{3}+12a^{2}-8a-16}
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}