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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

\frac{1}{1 0 ^{- 3}}

4 u^{2} + 25 = - 20 u

t^{2} - 10 t + 24 = 0

3 x + 5 = 8

x^{2} - 10 x + 21 = x^{2} - 10 x + 21

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