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How do you simplify # ((x^3(y)/(xy^2))*((3x^2(y))/(8x^3))#?

Answer 1

Ethan Adkins

#(x^3y/(xy^2)) * (3x^2y)/(8x^3) = (3x)/8#

#(x^3y/(xy^2)) * (3x^2y)/(8x^3)#

#=color(red)((x^3*y)/(x*y*y))* color(blue)((3*x*x*y)/(8*x^3))#

#=color(red)((cancel(x^3)*y)/(x*y*y))* color(blue)((3*x*x*y)/(8*cancel(x^3)))#

#=color(red)((y)/(cancel(x) * y * y)) * color(blue)((3 * cancel(x) * x * y)/(8))#

#=color(red)(cancel(y))/(cancel(y) * cancel(y)) * color(blue)((3 * x * cancel(y)))/(8)#

# = (3x)/8#

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Answer 2

Jace Anderson

To simplify the expression ((x^3(y)/(xy^2))*((3x^2(y))/(8x^3)), we can cancel out common factors in the numerator and denominator.

First, cancel out the common factors in the numerator: x^3 * 3x^2 = 3x^5

Next, cancel out the common factors in the denominator: xy^2 * 8x^3 = 8x^4y^2

The simplified expression is: (3x^5)/(8x^4y^2)

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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.