Question 79496
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Problem is 
Science and medicine. The combined resistance 
of two resistors R1 and R2 in a
parallel circuit is given by the formula 

{{{Rt = 1/(1/R1 + 1/R2)}}}

Write the {{{1}}} on top as {{{1/1}}} to
make everything fractions:

{{{Rt = (1/1)/((1/R1 + 1/R2))}}}

The LCD of all the denominators is {{{R1*R2}}}.

Write that as {{{(R1*R2)/1}}}

Multiply top and bottom of right side by that

{{{Rt = ( (R1*R2)/1)/((R1*R2)/1)}}}{{{(1/1)/((1/R1 + 1/R2))}}}

The top just becomes {{{R1*R2}}}

{{{Rt = (R1*R2)/(((R1*R2)/1)(1/R1 + 1/R2))}}}

In the bottom we distribute the {{{((R1*R2)/1)}}}
into the right parentheses:

{{{Rt = (R1*R2)/( ((R1*R2)/1)(1/R1) + ((R1*R2)/1)(1/R2))}}}

The R1's cancel in the first term on the bottom and the
R2's cancel in the second term on the bottom, so we end 
up with just

{{{Rt = (R1*R2)/(R2+R1)}}}

You might want to reverse the the terms in the bottom
so they will be in numerical order:

{{{Rt = (R1*R2)/(R1+R2)}}}

which says:

"The total resistance of two resistors in parallel is
the product of their resistances over their sum."

Edwin</pre>