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{31}{\frac{25}{\frac{12}{25}}}

w + w + (2 w - 2) + (2 w - 2) = 11

3^{8}

505

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))