Question

Assume

g(x) = (x − 2) / (x + 9)

Simplify the following expression.
(g(a + t) − g(a)) / t


WebAssign gave me the answer but I don't understand the steps to how it found the answer. If someone could explain everything that would be awesome, thanks!

Answer 1

first of all, what's g(a+t)?

Answer 2

ankit, please don't give away the answer.

Answer 3

((a+t-2)/(a+t+9) -(a-2)/(a+9))/t Now you can solve from here

Answer 4

Hmm... I had gotten to that point but blanked on what to do from there. After staring at it and writing it over and over I remembered to get those like denominators then solve from there.... but I ended up with

9T - 2a - 18
----------
t

which is wayyy off from the correct answer...

Answer 5

for simplification you can substitute a+9 with X...makes calculation easier

Answer 6

...took me enough times to do the subtraction right. FINALLY I have 11t....

Could I ask however what happened to the original t that this was all over? The correct answer is

\[(11t) \div((a+9)(a+t+9))\]

but how did we cancel out that original T in the bottom?

(Thanks for the continued responses you've been giving by the way)

Answer 7

Wait... we got rid of the unlike denominators before so t(a+9(a+t+9) became out denominator.... then we knocked out the t so it's really

(11) / (a+9)(a+t+9)

......I get it it now... kind of... yeah.

Thanks!