SOLUTION: {{{((((x-2))/((x+2)) + ((x-1))/((x+1)))) /(( x/((x+1))-((2x-3))/x))}}}

The LCD of all 4 denominators is , we put 
it over itself and have ,
but so it will have 4 levels, we put 1's under each,
like this .

Next we multiply this by the original complex fraction:

·

Next we distribute the red fractions into the BIG parentheses
to remove just the BIG parentheses:



In the upper left we cancel the (x+2)'s
In the upper right we cancel the (x+1)'s
In the lower left we cancel the (x+1)'s
In the lower right we cancel the x's



Now we have this:



Multiply the red factors:



Multiply the red ones into the black ones and make
them all black:



Collect like terms within the parentheses:



Remove the parentheses:



Edwin