SOLUTION: a) Solve for n and check: n+6 over 3 - n-3 over 2 = 2 b) Perform the indicated operation and express the result in lowest terms: x²-9 over x-3 times 4x+8 over x²+5x+6

Algebra ->  Equations -> SOLUTION: a) Solve for n and check: n+6 over 3 - n-3 over 2 = 2 b) Perform the indicated operation and express the result in lowest terms: x²-9 over x-3 times 4x+8 over x²+5x+6      Log On


   

Question 197468: a) Solve for n and check:
n+6 over 3 - n-3 over 2 = 2
b) Perform the indicated operation and express the result in lowest terms:
x²-9 over x-3 times 4x+8 over x²+5x+6
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a) Solve for n and check:
%28%28n%2B6%29%29%2F3 - %28%28n-3%29%29%2F2 = 2
Multiply by 6 to get rid of the denominators
6*%28%28n%2B6%29%29%2F3 - 6*%28%28n-3%29%29%2F2 = 6(2)
Cancel out the denominators
2(n+6) - 3(n-3) = 12
:
2n + 12 - 3n + 9 = 12
;
-n + 21 = 12
:
-n = 12 - 21
:
-n = -9
Multiply both sides by -1; (n has to be positive)
n = +9
:
Check solution in original equation; substitute 9 for n
%28%289%2B6%29%29%2F3 - %28%289-3%29%29%2F2 = 2
%28%2815%29%29%2F3 - %28%286%29%29%2F2 = 2
5 - 3 = 2
:
:
b) Perform the indicated operation and express the result in lowest terms:
%28%28x%5E2-9%29%29%2F%28%28x-3%29%29 * %28%284x%2B8%29%29%2F%28%28x%5E2%2B5x%2B6%29%29
Factor
%28%28x-3%29%28x%2B3%29%29%2F%28%28x-3%29%29 * %284%28x%2B2%29%29%2F%28%28x%2B3%29%28x%2B2%29%29 = 4
Look at this, everything cancels leaving just 4