Question

Help solving inequality: 0< 1/x-3 + 2/x-9

How would I do that in steps, I believe they want me to find domain only. Please show me steps.

Answer 1

this is really a drag. you are going to have to add these up . no avoiding it

Answer 2

you get
\[0<\frac{1}{x-3}+\frac{2}{x-9}\]
\[0<\frac{x-9+2(x-3)}{(x-3)(x-9)}\]
\[0<\frac{3x-15}{(x-3)(x-9)}\]
\[0<\frac{3(x-5)}{(x-3)(x-9)}\]

Answer 3

zeros are at 3, 5 and 9
so you have to check the following intervals:
\[(-\infty, 3)\]
\[(3,5)\]
\[(5,9)\] and
\[(9,\infty)\]

Answer 4

if you check you will see it is positive on
\[(3,5)\cup (9,\infty)\]

Answer 5

You deserve 10 medals! Do you tutor on skype by any chance?