# What are the excluded values and how do you simplify the rational expression #(3y-27)/(81-y^2)#?

Simplified

You are not mathematically 'allowed' do divide by 0. If this situation exists the equation / expression is called 'undefined'

When you get very close to a denominator of 0 the graph forms asymptotes.

so by substitution we have:

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The excluded values are the values of y that make the denominator equal to zero. In this case, the denominator is 81-y^2, so the excluded values are y = 9 and y = -9. To simplify the rational expression (3y-27)/(81-y^2), we can factor the denominator as (9+y)(9-y). Then, we can cancel out the common factor of (y-9) in the numerator and denominator, resulting in (3)/(9+y).

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