can someone help me on a math problem plz.......?

Question

well i dont know how to simplify expressions can someone plz.. help me on a probem plz explain how to do it..here it goes

12xy^4+16x^2y+4xy
----------------------------
4xy

Answer 1

Since they want you to "reduce" the fraction
look for "numbers" and also "variables"
that you can cancel on top and bottom

Constants are 12, 16, 4 on the top
and 4 on the bottom. You can divide all these numbers
by 2, but 4 is the largest common factor.
So try dividing through by 4 to get

4(3xy^4 + 4x^2y + xy)
----------------------------------------
4xy

Cancel 4 on top and bottom to get

3xy^4 + 4x^2y + xy
--------------------------
xy

Again, try factoring out xy to see if it cancels on top and bottom

xy (3y^3 + 4x + 1)
-------------------------
xy

so divide top and bottom by xy (since xy cannot be 0)

leaves
3y^3 + 4x + 1

To check your work
try plugging in x = 2 and y = 2
into both the "original" fraction and the "final" answer
to see if you get the same values for both (if not
they are not equivalent fractions and not reduced correctly)

(You can't always check by using x = 1 or y = 1,
because the exponents can be wrong
but the values could still come out the same.
So I use x or y = 2.)

Original fraction with x =2, y = 2:

12 (2)(16) + 16 (4)(2) + 16
-----------------
16

equals 24 + 8 + 1 = 33

Final fraction with x = 2, y = 2

3y^3 + 4x + 1
3(8) + 8 + 1 = 33

This is problably correct (unless x and y were written in
place of each other. If both variable are = 2, this could
produce the same answer. But it can be a quick way
to check for exponent or arithmetic or sign errors.)

Answer 2

I would try to factor a 4xy out of the denominator so you can get rid of the denominator, making the new problem:
(4xy(3y^3+4x+1))/4xy, by reducing both the top and the bottom by 4xy, you are left with:
3y^3+4x+1 as your answer.

Answer 3

3y^3+4x+1