Need help with math problem

[dlawrence]

Here is the problem:

(c-d)/((1/d)-(1/c))

Possible answers are:

a. (c-d)/dc

b. dc/(c-d)

c. dc

d. -dc

e. 1/dc

 

[dlawrence]

(c-d) * [(cd)/(c-d)] = cd or dc

Thanks so much, do you think you could tell me the name of that rule?

 

[soroban]

Hello, dlawrence!

\(\displaystyle \dfrac{c-d}{\frac{1}{d} - \frac{1}{c}}\)

. . \(\displaystyle (a)\;\dfrac{c-d}{cd} \qquad (b)\;\dfrac{cd}{c-d} \qquad (c)\;cd \qquad (d)\;-cd \qquad (e)\;\dfrac{1}{cd}\)

Why can't they write varaibles in alphabetical order?

Multiply the fraction by \(\displaystyle \frac{cd}{cd}\!:\;\;\dfrac{cd(c-d)}{cd\left(\frac{1}{d} - \frac{1}{c}\right)}\;=\;\dfrac{cd(c-d)}{c - d} \;=\;cd \quad\text{ . . . answer (c )} \)