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How do you solve #(x-6)^2/x<0#?

Answer 1

Eva Adamson

#x in (-oo,0)#

even power so sign will not change

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Answer 2

Jameson Allen

To solve the inequality (\frac{(x - 6)^2}{x} < 0), we first find the critical points by setting the numerator and denominator equal to zero separately. This gives us (x - 6 = 0) and (x = 0). Next, we create a sign chart with these critical points and test intervals between them to determine where the expression is positive or negative. After analyzing the intervals, we find that the solution to the inequality is (x \in (-\infty, 0) \cup (0, 6)).

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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.

How do you solve #(x-6)^2/x&lt;0#?

How do you solve #(x-6)^2/x<0#?