Question

Solve 14/(x^2-3x) - 8/x > -10/(x-3)

Answer 1

Well you want to first open the brackets and get x on one side by itself

Answer 2

You have to also consider the separate cases of when x is positive and when its negative

Answer 3

rewrite the inequality as
14/(x^2-3x) - 8(x-3)/(x^2-3x) > -10x/(x^2-3x)

or

(14-8(x-3)+10x)/(x^2-3x) > 0

Answer 4

sorry i was away from my computer for a minute.

Answer 5

so then I have 38+2x/x^2-3x>0

Answer 6

@watchmath what do i do with this next

Answer 7

ok so you have (38+2x)/(x(x-3)) >0. Draw a number line and put the point x=-19, x=0, x=3 on it. Then check the sign of (38+2x),x, (x-3) on each subinterval and find out which subinterval that gives (38+2x)/(x(x-3)) is positive

Answer 8

Here are your answers.
x>3, that's your solution.
Integer solutions are.
x=-18
x=-17
x=-16

Answer 9

thank you both!