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)
2 Answers | Add Yours
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).
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