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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

a - 1

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

Apply the fraction rule:

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

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

\frac{5}{8} + \frac{4}{6}

\frac{( x ^{3} - 21 x - 20 )}{x + 4}

\frac{2 x + 6}{x + 3}

120 \div 30

5^{2^{2}}

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