Question

(a^2-5/a^3-1)-(a+1/a^2+a+1)
combine as indicated by the signs

Answer 1

well you can factor the denominator of the 1st fraction to which is the difference of 2 cubes

(a - 1)(a^1 + a + 1)

so your fractions are

\[\frac{a^2 - 5}{(a -1)(a^2 + a + 1)} - \frac{(a+1)}{(a^2 + a + 1)}\]

now get a common denominator...

\[\frac{a^2 - 5}{(a -1)(a^2 + a + 1} - \frac{(a -1)(a +1)}{(a-1)(a^2 + a + 1)}\]

now you can subtract the fractions...

you should simplify the numerator of the 2nd fraction 1st