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How do you simplify #(x^2-y^2)/(8y-8x)#?

Answer 1

Ethan Adkins

See a solution process below:

First, apply this rule to factor the numerator:

#a^2 - b^2 = (a + b)(a - b)#

#(x^2 - y^2)/(8y - 8x) => ((x + y)(x - y))/(8y - 8x)#

Next, factor a #color(red)(-8)# out of the denominator:

#((x + y)(x - y))/((-8 xx - y) + (-8 xx x)) => #

#((x + y)(x - y))/(-8(-y + x)) => #

#((x + y)(x - y))/(-8(x - y))#

Next, remove the common terms from both the denominator and the numerator:

#((x + y)color(red)(cancel(color(black)((x - y)))))/(-8color(red)(cancel(color(black)((x - y))))) =>#

#(x + y)/-8#

#-(x + y)/8#

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Answer 2

Nathan Axel

To simplify the expression (x^2-y^2)/(8y-8x), we can factor the numerator and denominator. The numerator can be factored as (x+y)(x-y), and the denominator can be factored as 8(y-x). Simplifying further, we get (x+y)(x-y)/-8(x-y). The common factor of (x-y) can be canceled out, resulting in (x+y)/-8. Therefore, the simplified form of (x^2-y^2)/(8y-8x) is (x+y)/-8.

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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.