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How do you solve the equation and identify any extraneous solutions for #3/(y+5) - 9/(y-5) = 6/(y^2-25)#?

Answer 1

Abigail Allen

#y=-11#
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Answer 2

Savannah Anderson

To solve the equation 3/(y+5) - 9/(y-5) = 6/(y^2-25), we first need to find a common denominator for the fractions. The common denominator is (y+5)(y-5).

Multiplying each term by the common denominator, we get: 3(y-5) - 9(y+5) = 6

Expanding and simplifying the equation, we have: 3y - 15 - 9y - 45 = 6 -6y - 60 = 6

Adding 60 to both sides, we have: -6y = 66

Dividing both sides by -6, we get: y = -11

To check for extraneous solutions, we substitute y = -11 back into the original equation: 3/(-11+5) - 9/(-11-5) = 6/((-11)^2-25) 3/(-6) - 9/(-16) = 6/(121-25) -1/2 + 9/16 = 6/96 -8/16 + 9/16 = 1/16

Since the equation holds true, there are no extraneous solutions. Therefore, the solution to the equation is y = -11.

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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.