# what is the difference of the following

#### nae

##### New member
5 - 3(x+7) 5minus3(x+7)
___ ____
x+2 x+2

so far i got 5/x+2 -3x+21/x+2
than i get lost after the first step

#### stapel

##### Super Moderator
Staff member
nae said:
5 - 3(x+7) 5minus3(x+7)
___ ____
x+2 x+2
I'm sorry, but I can't figure this one out. (For instance, is the second "5" meant to be a power on the "3(x + 7)"?)

Please reply using single-line formatting and grouping symbols to make your meaning clear.

Thank you.

Eliz.

#### stapel

##### Super Moderator
Staff member

nae said:
5/x+2 - 3(x+7)/x+2

i came up with 5/x+2 - 3x+21/x+2
is this answer correct?
FYI: It is best to post replies to questions within the original thread, so that the questions and answers are together and people know what it going on in the "conversation". Thank you.

What you have posted means the following:

. . . . .$$\displaystyle \L \frac{5}{x}\,+\,2\,- \,\frac{3(x\,+\,7)}{x}\,+ \,2$$

I will guess that you mean this:

. . . . .$$\displaystyle \L \frac{5}{x\,+\,2}\,-\,\frac{3(x\,+\,7)}{x\,+\,2}$$

If so, then it appears that you have expanded the one numerator correctly:

. . . . .$$\displaystyle \L \frac{5}{x\,+\,2}\,-\,\frac{3x\,+\,21}{x\,+\,2}$$

Now you need to combine the two fractions.

Eliz.

#### nae

##### New member
what is the diffrence of the following

when i add the two together i got 19/2 is this correct.

#### Denis

##### Senior Member
. . . . .$$\displaystyle \L \frac{5}{x\,+\,2}\,-\,\frac{3x\,+\,21}{x\,+\,2}$$

nae: when i add the two together i got 19/2 is this correct.

Where did the x's go, nae? How did you get that?
I suggest you go back to basics...with a teacher/tutor #### nae

##### New member
what am i doing wrong if thats is not the answer i subtracted 21-5 = 16+3=19 i cancell the x out which gave me the 2.

#### soroban

##### Elite Member
Hello, nae!

They already gave you a common denominator.
Exactly where is your difficulty?

$$\displaystyle \L\;\frac{5}{x\,+\,2} - \frac{3(x\,+\,7)}{x\,+\,2}$$

We can make one fraction: $$\displaystyle \L\:\frac{5\,-\,3(x\,+\,7)}{x\,+\,2}$$

Simplify: $$\displaystyle \L\,\frac{5\,-\,3x\,-\,21}{x\,+\,2} \;= \;\frac{-3x\,-\,16}{x\,+\,2}$$

#### stapel

##### Super Moderator
Staff member
nae said:
what am i doing wrong if thats is not the answer i subtracted 21-5 = 16+3=19 i cancell the x out which gave me the 2.
Since 21 - 5 does not equal 19, I'm afraid I do not follow. It would help if you showed your work, step-by-step, as has been provided in replies to you.

Note: One can cancel only factors, not terms inside factors. Just as one could not cancel the 2's in 12/25 to somehow get 1/5, so also one cannot cancel the x's in (-3x - 16)/(x + 2) to somehow get (-3 - 16)/(1 + 2).

As has been suggested, your level of confusion is such that you would likely profit greatly from an in-depth conference with your instructor and/or your academic advisor. There appear to be gaps in your mathematical background which are hindering you, and it would be a shame to see that situation remain unrectified.

My best wishes to you.

Eliz.