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partial fraction decomposition of $\frac{k^4}{(a\, k^3-1)^2}$

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List Question

Inequality with cyclic sum

What's wrong with my workings? Adding fractions question.

An equality involving trigonometry

Is it possible to manipulate: $\frac{x^2 -2}{x+1}$ such that the numerator has a lower power than the denominator?

How to solve a system of equations with varying exponents?

Inequality in three variables $a,b,c$ given $abc\geq 1$

Nice inequality with a,b,c,d

$p_1+\cdots+p_k=1$, can those be written as rational numbers $p_1=n_1/m,~p_2=n_2/m,~\ldots,~p_k=n_k/m$?

Calculate $\tan^2{\frac{\pi}{5}}+\tan^2{\frac{2\pi}{5}}$ without a calculator

Find $\arctan(\frac{1}{3})+\arctan(\frac{1}{9})+\arctan(\frac{7}{19})$

Logic behind absolute value problem

Sum of fractions given sum of denominators and count

Remainder and long division

Continued fraction in 8th root------ any simpler approach?

partial fraction decomposition of $\frac{k^4}{(a\, k^3-1)^2}$

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