Add or subtract as indicated.

1. b/b-1 + 2b/b^2 -1

2. a-1/a+1 + a+1/a-1

Please help me to understand how to find these answers. Thanks!

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- Apr 30th 2007, 06:10 AMcutiepi_86Algebra...Adding & Subtracting Fractions
Add or subtract as indicated.

1. b/b-1 + 2b/b^2 -1

2. a-1/a+1 + a+1/a-1

Please help me to understand how to find these answers. Thanks! - Apr 30th 2007, 06:15 AMtopsquark
I presume this is

b/(b - 1) + 2b/(b^2 - 1)

Please use parenthesis!

Like adding any other kind of fraction, you need a common denominator. So factor

b^2 - 1 = (b + 1)(b - 1)

The first fraction only has a b - 1 in its denominator, so we need to multiply top and bottom by b + 1:

b/(b - 1) * (b + 1)/(b + 1) + 2b/[(b + 1)(b - 1)]

= b(b + 1)/[(b + 1)(b - 1)] + 2b/[(b + 1)(b - 1)]

= [b(b + 1) + 2b]/[(b + 1)(b - 1)]

= [b^2 + b + 2b]/[(b + 1)(b - 1)]

= [b^2 + 3b]/[(b + 1)(b - 1)]

= [b(b + 3)]/[(b + 1)(b - 1)]

-Dan - Apr 30th 2007, 06:19 AMtopsquark
Again, this is

(a - 1)/(a + 1) + (a + 1)/(a - 1)

right?

To get a common denominator, we need to multiply the first fraction by (a - 1)/(a - 1) and the second fraction by

(a + 1)/(a + 1):

(a - 1)/(a + 1) * (a - 1)/(a - 1) + (a + 1)/(a - 1) * (a + 1)/(a + 1)

= [(a - 1)^2]/[(a + 1)(a - 1)] + [(a + 1)^2]/[(a + 1)(a - 1)]

= [(a - 1)^2 + (a + 1)^2]/[(a + 1)(a - 1)]

= [a^2 - 2a + 1 + a^2 + 2a + 1]/[(a + 1)(a - 1)]

= [2a^2 + 2]/[(a + 1)(a - 1)]

= [2(a^2 + 1)]/[(a + 1)(a - 1)]

-Dan - Apr 30th 2007, 06:23 AMcutiepi_86
Thanks so much Dan!