Question 80194
<pre><font face = "lucida console" size = 4><b> 
{{{(n-5)/(6n-6) = 1/9 - (n-3)/(4n-4)}}}

I tried to my best to type the fractions so I hope this 
makes sense. Can you help me solve this? 

{{{(n-5)/(6(n-1)) = 1/9 - (n-3)/(4(n-1))}}}

The LCD of all the denominators is {{{36(n-1)}}}

So put the LCD over 1  {{{(36(n-1))/1}}}

{{{(36(n-1))/1}}}{{{(n-5)/(6(n-1))}}} = {{{(36(n-1))/1}}}{{{1/9}}} - {{{(36(n-1))/1}}}{{{(n-3)/(4(n-1))}}}

On the left side you can cancel the 6 into the 36 and 
end up with

{{{6(n-5)}}} = {{{(36(n-1))/1}}}{{{1/9}}} - {{{(36(n-1))/1}}}{{{(n-3)/(4(n-1))}}}

In the first term on the right you can cancel the 9 
into the 36 and end up with

{{{6(n-5)}}} = {{{4(n-1)}}} - {{{(36(n-1))/1}}}{{{(n-3)/(4(n-1))}}}

In the last term on the right you can cancel both the 4 
into the 36 and the (n-1)'s and now you have just

{{{6(n-5)}}} = {{{4(n-1)}}} - {{{9(n-3)}}}

Remove the parentheses by distributing:

{{{6n-30}}} = {{{4n-4}}} - {{{9n + 27}}}  

{{{6n - 30 = -5n+23}}} 

{{{11n = 53}}}

{{{n = 53/11}}}

Edwin</pre>