SOLUTION: 1. (2x^2 + x - 3)/9 times (x + 1)^2/(2x^2 + 5x + 3) 2. 1/(25 - y^2) divided by (6 - 3y)/y^2 - 7y + 10) 3. abc/(a^2 - 3a - 10) divided by a^2/(a^2 - 25) times (4 - a^2/9b^2 -

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: 1. (2x^2 + x - 3)/9 times (x + 1)^2/(2x^2 + 5x + 3) 2. 1/(25 - y^2) divided by (6 - 3y)/y^2 - 7y + 10) 3. abc/(a^2 - 3a - 10) divided by a^2/(a^2 - 25) times (4 - a^2/9b^2 -       Log On


   

Question 256883: 1. (2x^2 + x - 3)/9 times (x + 1)^2/(2x^2 + 5x + 3)
2. 1/(25 - y^2) divided by (6 - 3y)/y^2 - 7y + 10)
3. abc/(a^2 - 3a - 10) divided by a^2/(a^2 - 25) times (4 - a^2/9b^2 - 4 divided by (abc + 5bc)/(3ab - 2a)
4. (n^2 + 5n + 6)/(n^2 + 7n + 12 times (n^2 + 9n + 20/(n^2 + 11n + 30)
Found 2 solutions by richwmiller, drk:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Reminder :
one problem per submission
limit 4 submissions daily
no similar problems

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
1. (2x^2 + x - 3)/9 times (x + 1)^2/(2x^2 + 5x + 3)
step 1 - factor all possible polynomials as
%282x+%2B+3%29%28x-1%29%2F9 * %28x+%2B+1%29%5E2%2F%28%282x%2B3%29%28x%2B1%29%29
step 2 - cancel where needed as
%28%28x-1%29%2F9%29%2A%28x%2B1%29
which is simplified as
%28x%5E2-1%29%2F9
--
2. 1/(25 - y^2) divided by (6 - 3y)/y^2 - 7y + 10)
step 1 - factor all possible polynomials as
1%2F%285%2By%29%285-y%29%29 / %283%282-y%29%29%2F%28%28y-5%29%28y%2B3%29%29+
step 2 - multiply by reciprocal to get
1%2F%285%2By%29%285-y%29%29 * * %28y%2B3%29%2F%283%2A%282-y%29%29
-%28y%2B3%29%2F%28-3y%5E2-3y%2B10%29
--
3. abc/(a^2 - 3a - 10) divided by a^2/(a^2 - 25) times (4 - a^2/9b^2 - 4 divided by (abc + 5bc)/(3ab - 2a)
step 1 - factor all possible polynomials
abc%2F%28%28a-5%29%28a%2B2%29%29 / a%5E2%2F%28%28a%2B5%29%28a-5%29%29 * %282%2Ba%29%282-a%29%2F%28%283b%2B2%29%283b-2%29%29 / bc%28a%2B5%29%2F%283b-2a%29
which becomes
abc%2F%28%28a-5%29%28a%2B2%29%29 * %28%28a%2B5%29%28a-5%29%29%2Fa%5E2 * %283b-2a%29%2Fbc%28a%2B5%29 * %282%2Ba%29%282-a%29%2F%28%283b%2B2%29%283b-2%29%29
step 2 - reduce as needed to get
%28a%2B5%29%282-a%29%283b-2a%29 / a%283b%2B2%29%283b-2%29
--
4. (n^2 + 5n + 6)/(n^2 + 7n + 12 times (n^2 + 9n + 20/(n^2 + 11n + 30)
step 1 -factor all possible polynomials to get
%28%28n%2B3%29%28n%2B2%29%29%2F%28%28n%2B3%29%28n%2B4%29%29 * %28%28n%2B4%29%28n%2B5%29%29%2F%28%28n%2B5%29%28n%2B6%29%29
this reduces nicely to
%28n%2B2%29%2F%28n%2B6%29