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How do you solve #5/(y-3) - 30/(y^2-9)= 1#?

Answer 1

Eva Adamson

#[(5(y + 3))/(y^2 - 9) ] - 30/(y^2 - 9) = 1#

5y + 15 - 30 = (y - 3)(y + 3)

5(y - 3) = (y - 3)(y + 3) -> 5 = y + 3 -> y = 2.

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Answer 2

Eva Abramson

To solve the equation 5/(y-3) - 30/(y^2-9) = 1, we can follow these steps:

Simplify the equation by finding a common denominator for the fractions. The common denominator is (y-3)(y+3), since (y^2-9) can be factored as (y-3)(y+3).
Multiply each term by the common denominator to eliminate the fractions.
Simplify the equation further by distributing and combining like terms.
Rearrange the equation to isolate the variable on one side.
Solve for y by applying the appropriate algebraic operations.

The solution to the equation will be the value(s) of y that satisfy the equation after following these steps.

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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.