Question 208394
When {{{1/(3K) + 1/(4K) = 1}}} what is the value of {{{K}}}?

 {{{1/(3K) + 1/(4K) = 1}}}  
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Write {{{1}}} as {{{1/1}}} so everything will be
a fraction.

 {{{1/(3K) + 1/(4K) = 1/1}}}

Put parentheses around all the terms on both sides:

 {{{(1/(3K)) + (1/(4K)) = (1/1)}}}

{{{LCD = red(12K)}}}, so write {{{red(12K)}}} as {{{red(((12K)/1))}}},
then multiply through by {{{red(((12K)/1))}}}

 {{{(1/(3K))red(((12K)/1)) + (1/(4K))red(((12K)/1)) = (1/1)red(((12K)/1)))}}}

 {{{(1/(3K))((12K)/1) + (1/(4K))((12K)/1) = (1/1)((12K)/1)}}}

Cancel:
         {{{4}}}            {{{3}}}
 {{{(1/(cross(3)cross(K)))((cross(12)cross(K))/1) + (1/(cross(4)cross(K)))((cross(12)cross(K))/1) = (1/1)((12K)/1)}}}

All that's left is:


{{{4+3=12K}}}

{{{7=12K}}}

Divide both sides by {{{12}}}

{{{7/12=12K/12}}}

{{{7/12=K}}}

Edwin</pre>