rwgturner

ok, so i've just entered college after taking a year off after high school. So I have COMPLETELY lost all my math skills.....so if you could run me throught the process of how to complete this question, it should clear up some of the others. Thanks!

Simplify:

(3/x) + [1/(x^2 + x)]
----------------------------
(1/x+1) - (1/x-1)

The answer in the book is :
(3x+4)(x-1)
--------------
-2x

Compendium

For the denominator, do you mean 1/(x + 1) - 1/(x - 1) or 1/x + 1 - 1/x + 1?

rwgturner

1/(x + 1) - 1/(x - 1)

sorry for the confusion

Compendium

What I would do is multiply the numerator and the denominator by (x+1)(x-1), which would eliminate the fractions in the denominator. Then you can simplify the numerator.

rwgturner

i still dont understand how you can just multiply both denominator and numerator. both the numerator and denominator are fractions, so i dont understand how the process works.

Compendium

Doing this is multiplying by 1, because (x+1)(x-1)/[(x+1)(x-1)]=1. For the numerator, you distribute (x+1)(x-1) across the terms. You do the same for the denominator.

[3/x + 1/(x(x+1))](x+1)(x-1)
-----------------------------------
[1/(x+1) - 1/(x-1)](x+1)(x-1)


3(x+1)(x-1)/x + (x-1)/x
-------------------------------
(x-1) - (x+1)


(3x^2+x-4)
----------------
-2x


(3x+4)(x-1)
--------------
-2x