x^5/56 Multiplied by 48/x^5?

Question

ok how will i solve this?
when i solved it i got 6 over 7

this other problem ...x^2-x-12/x^2+5x+6 multipled x^2+x-2/x^2-5x+4


i have no idea how to solve it : (

Answer 1

First cross reduce
Both x^5's reduce to 1.
then 48 becomes 6 and 56 becomes 7. So it's 6/7.

Frist, multiply staright across.
(x^2-x-12)(x^2+x-2)
(x^4+x^3-2x^2)+(-x^3-x^2+2x)+(-12x^2-12x+24)
COmbine like terms.
x^4-13x^2-10x+24
That is the top half of the equation, now multiply the bottom.
(x^2+5x+6)(x^2-5x+4)
(x^4-5x^3+4x^2)+(5x^3-25x^2-20x)+ (6x^2-30x+24)
Combine like terms
x^4+10x^3-15x^2-50x+24

So put top over bottom
(x^4-13x^2-10x+24)/(x^4+10x^3-15x^2-50x+24)
Simplify
(13x^2-x)/(10x^3-15x^2-5x)

Answer 2

I believe you are right with your first solution.

For the second, combine like terms to get:
(x^2 - 4x + 6 - 12/x^2) * (x^2 - 4x + 4 - 2/x^2)

Then multiply each term in the first by each term in the second expression. For example, x^2 times the second part is:
x^4 - 4x^3 + 4x^2 - 2
and -4x times the second part is:
-4x^3 + 16x^2 -16x - 8/x
and 6 times the second part is
6x^2 - 24x + 24 - 12/x^2
and finally, 12/x^2 times the second part is
-12 + 48/x - 48/x^2 - 24/x^4
adding like terms, we get:
x^4 -8x^3 + 26x^2 - 40x + 10 + 40/x - 60/x^2 - 24/x^4