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Domain of Rational expressions (m2-8m+16)(5m2+m). Can you give me the step by process of the exclueded values of m?

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2 Answers

Valery you have to copy the problem exactly as it appears in the original source!!
The expression, if it is a rational, should have division sign.
So, division by zero is not defined.

  m2 - 8m + 16
 ————————
     5m2 + m

5m2 + m ≠ 0
m(5m + 1) ≠ 0

m1 ≠ 0 

5m2 + 1 ≠ 0

m2 ≠ – 1/5

The domain of rational expression are all number out of intervals
 (– ∞, – 1/5) U (– 1/5, 0) U (0, + ∞)

 <—————o————o—————>
 – ∞      – 1/5          0            + ∞ 

Hi Valery -- factoring looks like (m-4)(m-4)m(5m+1) ... typically, domain exclusions are "zeros in the denominator" or "square roots of negative values" or "logs of non-positive numbers" ... looks like any "m" can be plugged in safely ... other tutors may notice something I've missed ... Wish you well :)