Question

Can someone help me solve this algebraically?
(x+2)/(x-8)>(x)/(x+5)

Answer 1

=(x+2)(x+5)>x(x-8) x\[\neq\]8,-5
=x^2 + 7x+10>x^2-8x
=15x>-10
=x>-2/3 where x\[\neq\]8

Answer 2

Thank you!

Answer 3

i think in interval notation it is
\[(-5,-\frac{2}{3})\cup (8,\infty)\]

Answer 4

you cannot multiply both sides by the variable so solve these, because you don't know if it is positive or negative

Answer 5

you have to start with
\[\frac{x+2}{x-8}-\frac{x}{x+5}>0\] and go from there

Answer 6

so i am afraid your first solution is incorrect. can you continue?

Answer 7

Ok. Well, your answer does look more like the examples in the book. I'm afraid I can't continue, I really don't know what i'm doing. What would I do next?

Answer 8

you have to subtract on the left.
\[\frac{(x+2)(x+5)-x(x-8)}{(x-8)(x+5)}>0\] then multiply out in the numerator and combine like terms

Answer 9

\[\frac{x^2+7x+10-x^2+8x}{(x-8)(x+5)}>0\]
\[\frac{15x+10}{(x-8)(x+5)}>0\]

Answer 10

now the zeros of the factors are at
\[-5,-\frac{2}{3},8\]so you have to make 4 intervals

Answer 11

\[(-\infty, -5),(-5,-\frac{2}{3}),(-\frac{2}{3},8),(8,\infty)\]

Answer 12

then check on one interval by picking a number for x and substituting in the expression to see if it is positive or negative. it will change signs over each interval. if you do that you will see that the answer i wrote above is correct.

Answer 13

Wow. That's wonderful! Thank you! I will check to make sure it is.

Answer 14

easiest number to check is at x = 0 on the interval
\[(-\frac{2}{3},8)\] if you replace x by 0 you get
\[\frac{10}{-8\times 5}\] which is surely negative. you want positive because you have greater than zero, so pick the appropriate intervals

Answer 15

Thank you. Did you happen to see my other question?
If the total weekly cost for a company to produce its product as a function of the number of units produced is given by the equation f(x)=2x+500, write an equation to represent the average cost per unit.

Answer 16

I'm suppose to write an equation and the answer someone else gave me was f(x)=2+(500/x). Does that look right?