Expert: Josh - 11/18/2003

Question
Thank you in advance for your help.  I have been out of school for eight years and none of this stuck in the first place!

3/x-1  divided by 2/x+7

Answer
Sarah,

I hate to say this, it gets boring after a while.
If I solve the problem as it reads, you wouldn't get the right answer. Please watch out for syntax error when you type maths expressions on the keyboard.

I think the question is meant to be
3/(x-1) divided by 2/(x+7),
In words: "three over (x-1)" divided by "two over (x+7)"

This is entirely different from
(3/x)-1 divided by (2/x)+7,
Read as: [(3 over x) minus 1] divided by [(2 over x) plus 7]

which, strictly speaking, is how your question should be interpreted. But this is not what you want.

Both can be done, but you obtain different results.

Solution:
In general, one fraction (A/B) divided by (C/D) equals (A/B) multiplied by the inverse (D/C).

Identify the follow in this example.
Let A=3, B=(x-1), C=2, D=(x+7).
So,
[3/(x-1)] / [2/(x+7)]   ...cf. (A/B)/(C/D)
=[3/(x-1)] * [(x+7)/2]  ...cf. (A/B)*(D/C)
=[3*(x+7)]/[2(x-1)]     ...cf. [A*D]/[B*C]
=(3x+21)/(2x-2) Final result is obtained by expansion.

Please remember to always include parentheses where they are needed.

Cheers.