# How do you simplify #(y-x)/(12x^2-12y^2)#?

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To simplify the expression (y-x)/(12x^2-12y^2), we can factor out a common factor of -1 from the numerator, resulting in -(x-y)/(12x^2-12y^2).

Next, we can factor the denominator as the difference of squares: 12x^2-12y^2 = 12(x^2-y^2) = 12(x+y)(x-y).

Now, we can cancel out the common factor of (x-y) in the numerator and denominator, leaving us with -(1)/(12(x+y)).

Therefore, the simplified form of (y-x)/(12x^2-12y^2) is -(1)/(12(x+y)).

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To simplify ( \frac{y - x}{12x^2 - 12y^2} ), you first factor out the common terms from the numerator and the denominator:

( \frac{y - x}{12x^2 - 12y^2} = \frac{-(x - y)}{12(x^2 - y^2)} )

Next, you recognize that (x^2 - y^2) is a difference of squares, so you can factor it as follows:

(x^2 - y^2 = (x + y)(x - y))

Substitute this factorization back into the expression:

( \frac{-(x - y)}{12(x + y)(x - y)} )

Finally, you cancel out the common factor ((x - y)) from the numerator and the denominator:

( \frac{-1}{12(x + y)} )

So, ( \frac{y - x}{12x^2 - 12y^2} ) simplifies to ( \frac{-1}{12(x + y)} ).

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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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