SOLUTION: Give the domain of r(x)= (-5x^2-5x)÷(sqrt 10-6x)

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Question 1146991: Give the domain of r(x)= (-5x^2-5x)÷(sqrt 10-6x)
Answer by ikleyn(52799) About Me  (Show Source):
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The domain in this case is the set of all real numbers x such that


    10-6x > 0    (1)


providing the expression in the denominator under the square root positive and non-zero.


This inequality (1) is equivalent to


    10 > 6x,   or  x < 10%2F6 = 5%2F3.


ANSWER.  The domain is  x < 5%2F3.