Question 707045: Can you please explain to me how to solve this equation? I have tried to do it for an hour and cannot get it.
8y^3-27 / 64y^3-1 x 16y^2+4y+1 / 4y^2-9
Im not sure how to make these sit on top of each other on here. But please someone help me!!!!
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! When I want to make an expressions sit on top of another, I use the special codes from this website. I write the algebraically correct expression
((8y^3-27)/(64y^3-1))*((16y^2+4y+1)/(4y^2-9))=
and wrap it between three {'s and 3 }'s.
It's much easier to write it with just paper and pencil,
but when talking to or through a machine, you have to use precise language.
Your problem must be simplifying that rational expression and that requires factoring.
At this point you simplify by dividing both numerator and denominator by the same expressions,
which we do by crossing out matching top and bottom expressions, saying that "they cancel each other."
=
NOTES:
1) You have to remember that there are special products that result in a difference of squares, and in difference or sum of cubes.
 where  and  can be any mathematical expression.
Also,  and
 , where the quadratic polynomials
 and  cannot be factored further.
2) Factoring is a skill essential to math survival, and it requires practice. You thought you were done with polynomials, but factoring keeps coming back to haunt you, all the way through calculus and beyond. I found it the hard way when I was your age.
3) Parentheses are sometimes needed.
 , but if you key into your calculator
10-1/9-1= , your calculator, who knows and obeys the rules of order of operations, correctly interprets it as
 =8.88888...
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