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

The solution to 2/(a+2)+1/a+(a-1)/(a^2+2a) is (4a+1)/(a(a+2))

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

simplify

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

\frac{4 a + 1}{a ( a + 2 )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

2 a + a + 2 + a - 1 : 4 a + 1

= \frac{4 a + 1}{a ( a + 2 )}

x^{10} - 10 x^{6} + 9 x^{2}

(x + 4) (x + 2) (x - 1) (x - 3)

27 - 125 a^{3} - 135 a + 225 a^{2}

(- x + \frac{1}{5} - x^{3}) - (\frac{1}{2} x - x^{3} - \frac{4}{5})

lo g_{10} (a^{3}) b^{2} \cdot c^{5}

What is 2/(a+2)+1/a+(a-1)/(a^2+2a) ?
The solution to 2/(a+2)+1/a+(a-1)/(a^2+2a) is (4a+1)/(a(a+2))