SOLUTION: Good afternoon, I need some help with this problem please. I been stuck on it for a week now. My text book is of no help, not enough examples. Thank you for your time. VR First

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Good afternoon, I need some help with this problem please. I been stuck on it for a week now. My text book is of no help, not enough examples. Thank you for your time. VR First      Log On


   

Question 168327This question is from textbook
: Good afternoon, I need some help with this problem please. I been stuck on it for a week now. My text book is of no help, not enough examples. Thank you for your time.
VR
First question: 1/x^2-36}-{x+3/x^2-7x+6
Second questoin: 16 minus 1 over y^2 over 4 plus 1 over y

"1/x^2-36 is a fraction as is x+3/x^2-7x+6 I am to subract and then simplify if possible. It is asking for page number of my text this is in. This is a question the teacher gave me that is not in the text.
Thank you This question is from textbook

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
First question: 1/x^2-36}-{x+3/x^2-7x+6
1%2F%28%28x%5E2-36%29%29 - %28%28x%2B3%29%29%2F%28%28x%5E2-7x%2B6%29%29
Note that the 1st denominator is the "difference of squares"
2nd denominator can be factored also;
1%2F%28%28x-6%29%28x%2B6%29%29 - %28%28x%2B3%29%29%2F%28%28x-6%29%28x-1%29%29
The common denominator is(x-6)(x+6)(x-1)
we have:
%28%28x-1%29+-+%28x%2B3%29%28x%2B6%29%29%2F%28%28x-6%29%28x%2B6%29%28x-1%29%29 = %28%28x-1%29-%28x%5E2%2B9x%2B18%29%29%2F%28%28x-6%29%28x%2B6%29%28x-1%29%29 = %28%28x-1-x%5E2-9x-18%29%29%2F%28%28x-6%29%28x%2B6%29%28x-1%29%29; removing brackets changes signs
Combining like terms;
%28%28-x%5E2+-+8x+-+19%29%29%2F%28%28x-6%29%28x%2B6%29%28x-1%29%29 = %28-1%28x%5E2+%2B+8x+%2B+19%29%29%2F%28%28x-6%29%28x%2B6%29%28x-1%29%29 = -%28%28x%5E2+%2B+8x+%2B+19%29%29%2F%28%28x-6%29%28x%2B6%29%28x-1%29%29

Second question: 16 minus 1 over y^2 over 4 plus 1 over y
16+-+%281%2Fy%5E2%29%29
----------
4+%2B+%281%2Fy%29
:
We want each written as a single fraction:
%28%2816y%5E2+-+1%29%29%2Fy%5E2
----------
%28%284y+%2B+1%29%29%2Fy
:
Invert the dividing fraction and multiply
%28%2816y%5E2+-+1%29%29%2Fy%5E2 * y%2F%28%284y%2B1%29%29
:
16y^2 - 1 is the difference of squares, factor that to
%28%284y-1%29%284y%2B1%29%29%2Fy%5E2 * y%2F%28%284y%2B1%29%29
;
Some simple canceling and you have:
%28%284y-1%29%29%2Fy
:
:
"1/x^2-36 is a fraction as is x+3/x^2-7x+6 I am to subtract and then simplify if possible.
1%2F%28%28x%5E2-36%29%29 - %28%28x%2B3%29%29%2F%28%28x%5E2-7x%2B6%29%29
;
This is exactly the same as the 1st problem