Question

This is a three part question:
f(x) = (5x+3)/(4x-9) g(x) = 3x/(4x-9)

(f+g) (x) = ?
domain of f+g = ?
(f/g) (x) = ?
domain of (f/g) = ?

Answer 1

(f+g) (x) is the same as:
[(5x+3)/(4x-9)] +[(3x/4x-9}]
you have a common denominator so it is easy for you to perform the operation. try solving it from where I left off.

Answer 2

(8x+3)/(4x-9)?

Answer 3

yes

Answer 4

ya! now what do you know about domains and ranges?

Answer 5

that the x value can not produce 0 in the denominator?

Answer 6

for a rational/fraction, the thing to understand is THAT, the denominator CANNOT be zero, \(\large
\frac{0}{25}=0,\ but \frac{25}{0}=undefined
\)

Answer 7

yes

Answer 8

so, the domain is those values for X, where X doesn't produce a zero in the denominator

Answer 9

ok so...could this be all real numbers?

Answer 10

well, one sec

Answer 11

\(\large
4x-9=0 \implies x=\frac{9}{4}
\)

Answer 12

so, that "x" would give a 0, thus it cannot be part of the domain :)

Answer 13

oh ok so could I say x =/ 9/4 or would I say x< 9/4 and x > 9/4

Answer 14

and by =/ i mean \[x \neq 9/4\]

Answer 15

\(
(-\alpha, \frac{9}{4}) (\frac{9}{4}, +\alpha);\ x\ne \frac{9}{4}
\)

Answer 16

thereabouts

Answer 17

you got it , that's a big gambit

Answer 18

ok so how would i divide (5x+3) by 3x?

Answer 19

ohh the second one, one sec

Answer 20

well, tis simple really, when you have fractions as numerator and denominator, all you do is FLIP UPSIDE-DOWN the denominator fraction and multiply with the numerator :)

Answer 21

multiplication is a simple 'straight across' multiplication

Answer 22

so (5x+3)(4x-9) ?