What is 2/(a^2+2a+1)+3/(a^2-1) ?

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

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simplify 2/(a^2+2a+1)+3/(a^2-1)

simplify

\frac{2}{a ^{2} + 2 a + 1} + \frac{3}{a ^{2} - 1}

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

Solution steps

\frac{2}{a ^{2} + 2 a + 1} + \frac{3}{a ^{2} - 1}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

2 (a - 1) + 3 (a + 1) : 5 a + 1

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

\frac{x}{2} + \frac{1}{3} = \frac{5}{6}

14 b^{2} + 39 b + 10

- 6 (1 + 2 x) \geq 6 (2 x - 1) + 2 x

x^{2} - 5 x = - 3 x + 24

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