Question

Add: 4x+12 / x-2 - 2x+8 / -x+2
A. 2x+4 / x-2
B. 6x^2 +24x+8 / x^2-4
C. 6x+20 / x-2
D. -2
E. none of these.

Answer 1

I'm getting none of these. the answer i'm getting is 2(3x+10) / x-2

Answer 2

i guess that could be C then?

Answer 3

It is not clear what is being added. Use parenthesis to make it clear. Is it
\[
\frac{4x+12}{x-2} - \frac{2x+8}{-x+2}
\]?

Answer 4

\[
\frac{4x+12}{x-2} - \frac{2x+8}{-x+2} =
\frac{4x+12}{x-2} + \frac{2x+8}{x-2} =
\frac{4x+12+2x+8}{x-2} =
\frac{6x+20}{x-2}
\]

Answer 5

The problem expression as written is:
4x+(12/x)-2-2x -(8/x)+2
or
\[\frac{12}{x}+14 \]

Answer 6

Division has priority over addition and subtraction.

Answer 7

@aum that's what needed to be added. i got the same result.

Answer 8

If the answer to my first reply is yes, then the solution is in the second reply.
But without proper use of parenthesis it is not clear what is being divided by what.
In the textbook they may not have parenthesis because they print vertically where it is clear what the numerator is and what the denominator is. But here things are written horizontally and so you need to use parenthesis to group things properly so it is clear what is being divide by what.

Answer 9

Assuming yes to my first reply, the proper way to write this "horizontally" is:
(4x+12) / (x-2) - (2x+8) / (-x+2)

But if written "vertically", there is no need for parenthesis:\[
\frac{4x+12}{x-2} - \frac{2x+8}{-x+2}\]