Interval notation?

Question

Write the following in interval notation

3 / (x+10) - 6 / x^2+12x+20 > 0
(3 over x plus 10, minus 6 over x squared plus 12x plus 20 is greater than or equal to 0)

I got as far as factoring out the common denominator, (x+10)(x+2) and ended up with 3x/(x+10)(x+2) > 0

Is that the wrong form, the wrong answer, or both?

Any help is appreciated.

If you can provide steps, great, if you give the answer, I can just figure it out, I'm decently intuitive.

Answer 1

Add the fractions together by finding a common denominator. multiply the left fraction by the same thing on the top and the bottom so that both fractions have the same denominator. Then you can add the fractions to get one fraction.

Now think about how the signs of the numerator and the denominator make the fraction positive or negative. (hint: there are 2 ways they can combine to make a positive.)
Finally, determine when the numerator is positive and when it is negative. Do the same for the denominator.

Hopefully this is enough hints to help you figure it out. :-)

Answer 2

Are you sure that's the right exercise?
How can you solve x/y/z>0 ??
maybe is something like x>y/z>0

Check that.