What is 2/k+1/(k^2-1) ?

The solution to 2/k+1/(k^2-1) is (2k^2-2+k)/(k(k+1)(k-1))

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simplify 2/k+1/(k^2-1)

simplify

\frac{2}{k} + \frac{1}{k ^{2} - 1}

\frac{2 k ^{2} - 2 + k}{k ( k + 1 ) ( k - 1 )}

Solution steps

\frac{2}{k} + \frac{1}{k ^{2} - 1}

Least Common Multiplier of

k, k^{2} - 1 : k (k + 1) (k - 1)

Adjust Fractions based on the LCM

= \frac{2 ( k + 1 ) ( k - 1 )}{k ( k + 1 ) ( k - 1 )} + \frac{k}{k ( k + 1 ) ( k - 1 )}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{2 ( k + 1 ) ( k - 1 ) + k}{k ( k + 1 ) ( k - 1 )}

Simplify

2 (k + 1) (k - 1) + k : 2 k^{2} - 2 + k

= \frac{2 k ^{2} - 2 + k}{k ( k + 1 ) ( k - 1 )}

(3 x + 10) (3 x - 5)

1352

1525

(13 - 6) (213 - 5) + 1713

(x - 6) (- 3 x^{2} - 5 x - 2)

What is 2/k+1/(k^2-1) ?
The solution to 2/k+1/(k^2-1) is (2k^2-2+k)/(k(k+1)(k-1))