Question

i need help with this math question let f(x) = x+4/x+1, x is not equal -1, and g (x)=x-2/x-4, x is not equal to 4. find the set of values of x such that f(x) is equal to or less than G(x)

Answer 1

so it is asking you to solve f(x)<=G(x)

Answer 2

but I don't think G(x) has been given...
Is g(x)=G(x)?

Answer 3

or is there another type of relationship between g and G

Answer 4

g(x)is the same as G(x) sory just a typo

Answer 5

so you need to solve f(x)<=g(x)

Answer 6

that is
\[\frac{x+4}{x+1} \le \frac{x-2}{x-4}\]

Answer 7

First step: Make one side of the inequality 0 by moving one fraction to the other side by either addition/subtraction which ever one works in this case

Answer 8

alright and second step

Answer 9

combine the fractions

Answer 10

find the zeros of the fraction
and where the fraction doesn't exist

Answer 11

draw a number line
and test the intervals around each of those numbers

Answer 12

so first what do you get as the inequality after the first step

Answer 13

im stuck on that

Answer 14

\[f(x) \le g(x) \\ \text{ subtract } g(x) \text{ on both sides } f(x) -g(x) \le 0\]

Answer 15

now combine those fractions

Answer 16

2/-3

Answer 17

him you seem to be missing the variables...

Answer 18

you have
\[\frac{x+4}{x+1}-\frac{x-2}{x-4} \le 0\]

Answer 19

try combining the fractions on the left

Answer 20

is it
x-14/(x-4)(x+1)