Could you please help explain these two algebraic problems? Divide. 1. 2x^2 y (only the x is squared) -16xy^2 + 12xy / 2xy 2. -15xy + 10x / 5x

First, you need to use brackets at both numerators,
otherwise, the numerator of the 1st expression is just the term 12xy and the numerator
of the 12nd expression is just the term 10x.

You have to
simplify these two expressions.

We'll begin
with

(2x^2*y -16x*y^2 + 12xy) /
2xy

We'll write each term from numerator over the
denominator:

2x^2*y -16x*y^2 + 12xy / 2xy = 2x^2*y / 2xy -
16x*y^2 / 2xy + 12xy/ 2xy

We'll use the property of
division of two exponentials that have matching
bases:

x^a/x^b =
x^(a-b)

2x^2*y / 2xy = x^(2-1)*y^(1-1) = x*y^0 = x*1 =
x

16x*y^2 / 2xy =
(16/2)*x^(1-1)*y^(2-1)

16x*y^2 / 2xy = 8*x^0*y =
8y

12xy/ 2xy = (12/2)*x^(1-1)*y^(1-1) =
6

(2x^2*y -16x*y^2 + 12xy )/ 2xy = x - 8y +
6

We'll simplify the 2nd
expression:

(-15xy + 10x) / 5x = -15xy/5x +
10x/5x

-15xy/5x = -(15/5)x^(1-1)*y =
-3y

10x/5x = (10/5)*x^(1-1) =
2

(-15xy + 10x) / 5x = -3y +
2

The results of simplifying both expressions
are: 1) (2x^2*y -16x*y^2 + 12xy )/ 2xy = x - 8y + 6 and 2) (-15xy + 10x) / 5x = -3y +
2.