How do you multiply #(6x^2y^2)/(x-2) div (3xy^2)/(x-2)^2#?

Answer 1

#2x(x-2)=2x^2-4x#

#"to change division to multiplication note that"#
#•color(white)(x)a/b-:c/d=a/bxxd/c#
#rArr(6x^2y^2)/(x-2)-:(3xy^2)/((x-2)^2)#
#=(6x^2y^2)/(x-2)xx((x-2)^2)/(3xy^2)#
#"now "color(blue)"cancel"" common factors on the"# #"numerators/denominators of the fractions"#
#=(cancel(color(red)(6))^2cancel(color(blue)(x^2))^x cancel(color(magenta)(y^2))^1)/cancel((x-2)^1)xxcancel((x-2)^((x-2)))/(cancel(color(red)(3))^1cancel(color(blue)(x))^1cancel(color(magenta)(y^2))^1)#
#=(2x(x-2))/1=2x^2-4x#
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Answer 2

To multiply the given expressions, we can simplify the division by multiplying the first expression by the reciprocal of the second expression.

First, let's simplify the division by multiplying the numerator and denominator of the second expression by (x-2)^2:

(6x^2y^2)/(x-2) div (3xy^2)/(x-2)^2

= (6x^2y^2)/(x-2) * (x-2)^2/(3xy^2)

Next, we can cancel out common factors between the numerator and denominator:

= (6x^2y^2 * (x-2)^2) / (x-2 * 3xy^2)

= (6x^2y^2 * (x-2) * (x-2)) / (3xy^2 * (x-2))

= (6x^2y^2 * (x-2)) / (3xy^2)

Now, we can simplify further by canceling out common factors:

= (2x * (x-2)) / (y)

= (2x^2 - 4x) / y

Therefore, the simplified expression is (2x^2 - 4x) / y.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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