SOLUTION: Please help me solve this equation: I have to find the missing expression. The letter n is actually a question mark in my math book. {{{ 2x over x^3-3x^2 * x^2-x-6 over n = 1 o

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me solve this equation: I have to find the missing expression. The letter n is actually a question mark in my math book. {{{ 2x over x^3-3x^2 * x^2-x-6 over n = 1 o      Log On


   

Question 779410: Please help me solve this equation:
I have to find the missing expression.
The letter n is actually a question mark in my math book.
+2x+over+x%5E3-3x%5E2+%2A+x%5E2-x-6+over+n+=+1+over+3x+
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%282x%29%2F%28x%5E3-3x%5E2%29 * %28x%5E2-x-6%29%2Fn = 1%2F%283x%29
Factor
%282x%29%2F%28x%5E2%28x-3%29%29 * %28%28x-3%29%28x%2B2%29%29%2Fn = 1%2F%283x%29
Cancel x and (x-3)
%282%29%2F%28x%29 * %28%28x%2B2%29%29%2Fn = 1%2F%283x%29
which is:
%282%28x%2B2%29%29%2F%28nx%29 = 1%2F%283x%29
cross multiply
nx = 2(x+2) * 3x
nx = (2x + 4) * 3x
nx = 6x^2 + 12x
divide both sides by x
n = (6x + 12)
therefore our equation is:
%282x%29%2F%28x%5E3-3x%5E2%29 * %28x%5E2-x-6%29%2F%286x%2B12%29 = 1%2F%283x%29
:
:
:
You can check this out, factor the above
%282x%29%2F%28x%5E2%28x-3%29%29 * %28%28x-3%29%28x%2B2%29%29%2F%286%28x%2B2%29%29 = 1%2F%283x%29
Cancel x, (x-3), and (x+2)
%282%29%2F%28x%29 * 1%2F6 = 1%2F%283x%29
which is
2%2F%286x%29 = 1%2F%283x%29; confirms our answer of n = (6x+12)