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How do you combine #y/(y^2+y-12) - 3/(y^2+3y-18)#?

Answer 1

Ethan Adkins

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Answer 2

Savannah Anderson

To combine the given expressions, we need to find a common denominator. The denominators are (y^2+y-12) and (y^2+3y-18).

First, let's factorize the denominators: y^2+y-12 = (y+4)(y-3) y^2+3y-18 = (y+6)(y-3)

Now, we can see that the common denominator is (y+4)(y-3)(y+6).

Next, we need to rewrite the fractions with the common denominator: y/(y^2+y-12) = y/[(y+4)(y-3)] -3/(y^2+3y-18) = -3/[(y+6)(y-3)]

Now, we can combine the fractions by adding the numerators and keeping the common denominator: (y - 3) - 3(y + 4) / [(y+4)(y-3)(y+6)]

Simplifying the numerator: (y - 3) - 3(y + 4) = y - 3 - 3y - 12 = -2y - 15

Therefore, the combined expression is: (-2y - 15) / [(y+4)(y-3)(y+6)]

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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.