SOLUTION: Find the domain of the rational function: (y+5)/(y^2-5y)

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Question 684721: Find the domain of the rational function:
(y+5)/(y^2-5y)
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
You cannot divide by zero. So y^2 - 5y can't be zero.

If it were, then

y^2 - 5y = 0

y(y - 5) = 0

y = 0 or y - 5 = 0

y = 0 or y = 5

Those last two values make the denominator zero. So we must kick them out of the domain.

So the domain is the set of all real numbers except y can't be 0 or y can't be 5.

In set-builder notation, the domain is $\large \{y|y\in\mathbb{R},y\neq 0,y\neq 5\}$

In interval notation, the domain is $\large \left(-\infty, 0\right)\cup\left(0, 5\right)\cup\left(5, \infty\right)$

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Find the domain of the rational function:
(y+5)/(y^2-5y)
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The denominator cannot be zero.
Solve:
y^2-5y = 0
Factor:
y(y-5) = 0
y = 0 or y = 5
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Ans: Domain is All Real Numbers except y = 0 and y = -5.
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Cheers,
Stan H.
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