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How do you simplify #(x^2-y^2)/(5x^3)*(y^2)/(15x^2y^5)#?

Answer 1

Avery Alexander

#(x^2 - y^2)/(75x^5y^3)#

As per the question,

#(x^2 - y^2)/(5x^3) * y^2/(15x^2y^5)#

#(y^2(x^2 - y^2))/((5x^3)(15x^2y^5))#

#(y^2(x^2 - y^2))/(75x^5y^5)#

#((x^2 - y^2))/(75x^5y^3)# ... [#y^2# gets cancelled by #y^2# from #y^5# so #y^3# is remaining]

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Answer 2

Hazel Anglin

To simplify the expression (x^2-y^2)/(5x^3)*(y^2)/(15x^2y^5), we can combine the terms and simplify the exponents.

First, let's simplify the numerator (x^2 - y^2). This can be factored as (x + y)(x - y).

Next, let's simplify the denominator (5x^3)(y^2)(15x^2y^5). We can multiply the coefficients together to get 5 * 15 = 75. For the variables, we add the exponents when multiplying, so we have x^(3+2+2) * y^(1+5) = x^7 * y^6.

Now, we can rewrite the expression as (x + y)(x - y)/(75x^7y^6).

This is the simplified form of the given expression.

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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.