SOLUTION: A. Perform the indicated operation and express the result in simplest form: 3x+24 over x+2 times x²-6x-16 over x²-64 B. Solve for x: x+4 over 2 plus 2x over 3 equals 9

Algebra ->  Equations -> SOLUTION: A. Perform the indicated operation and express the result in simplest form: 3x+24 over x+2 times x²-6x-16 over x²-64 B. Solve for x: x+4 over 2 plus 2x over 3 equals 9      Log On


   

Question 199096: A. Perform the indicated operation and express the result in simplest form:
3x+24 over x+2 times x²-6x-16 over x²-64
B. Solve for x: x+4 over 2 plus 2x over 3 equals 9
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A. Perform the indicated operation and express the result in simplest form:
%28%283x%2B24%29%29%2F%28%28x%2B2%29%29 * %28%28x%5E2-6x-16%29%29%2F%28%28x%5E2-64%29%29
Factor, then everything cancels except 3
%283%28x%2B8%29%29%2F%28%28x%2B2%29%29 * %28%28x-8%29%28x%2B2%29%29%2F%28%28x-8%29%28x%2B8%29%29 = 3
;
:
B. Solve for x:
%28%28x%2B4%29%29%2F2 + %282x%29%2F3 = 9
Multiply by 6
6*%28%28x%2B4%29%29%2F2 + 6*%282x%29%2F3 = 6(9)
cancel denominators, results:
3(x+4) + 2(2x) = 54
:
3x + 12 + 4x = 54
:
7x = 54 - 12
:
7x = 42
x = 42%2F7
x = 6
:
Check solution in original equation
%28%286%2B4%29%29%2F2 + %282%2A6%29%2F3 = 9
10%2F2 + 12%2F3 = 9
5 + 4 = 9
: