# Correct the following.1. (b/b - 1) + (4b/b^2 - 1) 2. (a - 1/a + 1) + (a + 1/a-1) 3. (4/a - 5) - (1/5 - a)

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1. (b/b - 1) + (4b/b^2 - 1) = **(4 - b)/b**

Since b/b equals 1, the first set of parentheses is

(1 - 1) = 0

In the second set of parentheses,

4b/b^2 = 4/b

In order to subtract the 4/b - 1, change 1 to b/b.

4/b - b/b = (4 - b)/b

2. (a - 1/a + 1) + (a + 1/a - 1) = **2a**

-1/a + 1/a = 0

1 - 1 = 0

a + a = 2a

3. (4/a - 5) - (1/5 - a) = **(5a^2 - 26a + 20)/5a**

First distribute the minus sign to the second set of parentheses.

4/a - 5 - 1/5 + a

Rewrite with common denominators.

20/5a - 25a/5a - 1a/5a + 5a^2/5a

Combine the numerators.

20 - 25a - 1a + 5a^2 = 20 - 26a + 5a^2

Put this over the denominator 5a.

(5a^2 - 26a + 20)/5a

I read this to be a fraction added to a fraction.

b/(b-1) + 4b/(b^2-1) so i figured we needed a common denominator. If you multiply the first fraction top and bottom by b+1 you get b^2+b/(b^2-1) which can now be added to 4b/(b^2-1) which gives you b^2 +5b/(b^2-1). If you simplify it you get b(b+5/(b+1)(b-1).