Question

combine the following rational expressions:
(1)/(8x^3-1) - (1)/ (4x^2-1)

Answer 1

have you first tried facoting the denominators of both expresions

Answer 2

yes but you cant can you? thers no x with the 1

Answer 3

well, we have to notice something here:

recall these two formulas:


Difference of square: (a^2-b^2)=(a-b)(a+b)

Difference of cubes: a^3-b^3=(a-b)(a^2+ab+b^2)

Answer 4

now lets dissect your two denominators:

First, we have (8x^3-1)

can i write this as: (2x)^3-(1)^3

Answer 5

if i can (which i can) then it we can factor this using the formula i wrote up there, for the difference of cubes

Answer 6

The same goes for your other denominator ,expecet that one is a difference oif squares(i wrote the formula up there for this one two)

I can write (4x^2-1) as (2x)^2-(1)^2

Answer 7

now once you factor these two you will see what you need to multiply each fraction by inorder to subtract them

Answer 8

ok thanks!