What is 1/(5+5a)+1/(5-5a)-1/(10+10a^2) ?

The solution to 1/(5+5a)+1/(5-5a)-1/(10+10a^2) is (-5a^2-3)/(10(a+1)(a-1)(a^2+1))

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simplify 1/(5+5a)+1/(5-5a)-1/(10+10a^2)

simplify

\frac{1}{5 + 5 a} + \frac{1}{5 - 5 a} - \frac{1}{10 + 10 a ^{2}}

\frac{- 5 a ^{2} - 3}{10 ( a + 1 ) ( a - 1 ) ( a ^{2} + 1 )}

Solution steps

\frac{1}{5 + 5 a} + \frac{1}{5 - 5 a} - \frac{1}{10 + 10 a ^{2}}

Least Common Multiplier of

5 + 5 a, 5 - 5 a, 10 + 10 a^{2} : 10 (a + 1) (a - 1) (a^{2} + 1)

Adjust Fractions based on the LCM

= \frac{2 ( a - 1 ) ( a ^{2} + 1 )}{10 ( a + 1 ) ( a - 1 ) ( a ^{2} + 1 )} + \frac{- 2 ( a + 1 ) ( a ^{2} + 1 )}{10 ( a + 1 ) ( a - 1 ) ( a ^{2} + 1 )} - \frac{( a + 1 ) ( a - 1 )}{10 ( a + 1 ) ( a - 1 ) ( a ^{2} + 1 )}

Apply the fraction rule:

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

= \frac{2 ( a - 1 ) ( a ^{2} + 1 ) - 2 ( a + 1 ) ( a ^{2} + 1 ) - ( a + 1 ) ( a - 1 )}{10 ( a + 1 ) ( a - 1 ) ( a ^{2} + 1 )}

Simplify

2 (a - 1) (a^{2} + 1) - 2 (a + 1) (a^{2} + 1) - (a + 1) (a - 1) : - 5 a^{2} - 3

= \frac{- 5 a ^{2} - 3}{10 ( a + 1 ) ( a - 1 ) ( a ^{2} + 1 )}

\frac{2 m ^{2} + 4 m - 6}{4 m ^{2} + 16 m + 12}

(t^{2} - 1)^{2}

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

- 289

3 x^{3} + 5 x^{2} - 30 x - 50

What is 1/(5+5a)+1/(5-5a)-1/(10+10a^2) ?
The solution to 1/(5+5a)+1/(5-5a)-1/(10+10a^2) is (-5a^2-3)/(10(a+1)(a-1)(a^2+1))