# How do you solve #(x-2)^2/(x+4) < 0# ?

##### 2 Answers

#### Explanation:

Note that

When

#(x-2)^2/(x+4) = 0/6 = 0" "# which does not satisfy the inequality.

The only circumstance under which the rational expression is negative is if the denominator is negative:

#x+4 < 0#

Subtracting

#x < -4#

Note that when

#(x-2)^2/(x+4) < 0#

So it is sufficient that

#### Explanation:

George's explanation is very cool and on the money! Here's a different way to look at it.

When dealing with inequalities, if you multiply or divide by a negative number we have to flip the sign. In this case, we don't know if the denominator,

If we assume that

Going back to the inequality, if we now multiply both sides by

If you square a quantity, it is always positive, so the inequality above is invalid.

If you look at the second case and assume

Going back to the inequality, if we now multiply both sides by

Since we just, found

Here's a good video:

It's a little bit tricky :-)