What is (4a^2+3a+2)/(a^3-1)-(1-2a)/(a^2+a+1) ?

The solution to (4a^2+3a+2)/(a^3-1)-(1-2a)/(a^2+a+1) is (6a^2+3)/((a-1)(a^2+a+1))

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simplify (4a^2+3a+2)/(a^3-1)-(1-2a)/(a^2+a+1)

simplify

\frac{4 a ^{2} + 3 a + 2}{a ^{3} - 1} - \frac{1 - 2 a}{a ^{2} + a + 1}

\frac{6 a ^{2} + 3}{( a - 1 ) ( a ^{2} + a + 1 )}

Solution steps

\frac{4 a ^{2} + 3 a + 2}{a ^{3} - 1} - \frac{1 - 2 a}{a ^{2} + a + 1}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{4 a ^{2} + 3 a + 2}{( a - 1 ) ( a ^{2} + a + 1 )} - \frac{( 1 - 2 a ) ( a - 1 )}{( a - 1 ) ( a ^{2} + a + 1 )}

Apply the fraction rule:

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

= \frac{4 a ^{2} + 3 a + 2 - ( 1 - 2 a ) ( a - 1 )}{( a - 1 ) ( a ^{2} + a + 1 )}

Simplify

4 a^{2} + 3 a + 2 - (1 - 2 a) (a - 1) : 6 a^{2} + 3

= \frac{6 a ^{2} + 3}{( a - 1 ) ( a ^{2} + a + 1 )}

5 x + 11 < 6

\frac{3 x - 4}{2} > \frac{6 - 2 x}{3}

(- 10)^{2}

5 x + \frac{1}{2} - 4 < 8

3 x - 2 = - 7

What is (4a^2+3a+2)/(a^3-1)-(1-2a)/(a^2+a+1) ?
The solution to (4a^2+3a+2)/(a^3-1)-(1-2a)/(a^2+a+1) is (6a^2+3)/((a-1)(a^2+a+1))