simplify the difference.

Question

a^2-2a-8/ a^2-3a-10 - a^2-2a-3/ a^2+7a+6

Answer 1

To simplify the difference, we can combine like terms in the numerator and denominator separately.

Numerator:
(a^2 - 2a - 8) - (a^2 - 2a - 3)
= a^2 - 2a - 8 - a^2 + 2a + 3
= (-2a + 2a) + (a^2 - a^2) - 8 + 3
= 0 - 5
= -5

Denominator:
(a^2 - 3a - 10) - (a^2 + 7a + 6)
= a^2 - 3a - 10 - a^2 - 7a - 6
= (-3a - 7a) + (a^2 - a^2) - 10 - 6
= -10a - 16

Therefore, the simplified difference is:
(-5) / (-10a - 16) or simply 5 / (10a + 16)