1. Simplify

 

(L/(B-1)+L)/(l/(B-1))

First, add the fractions on top. Find common denominators:

 

(L/(B-1)+L((B-1)/(B-1)))/(L/(B-1))

 

 

Multiply out the second fraction on top.

 

(L/(B-1)+(LB-L)/(B-1))/(L/(B-1))

 

Add the tops on the top.

 

(L+(LB-L)/(B-1))/(L/(B-1))

 

The top simplifies to

 

(LB/(B-1))/(L/(B-1))

 

We are now ready to invert and multiply.

 

 

LB/(B-1)*(B-1)/L

Cancel

 

 

 

which simplifies to

 

B

 

Note that we could go straight from

 

(LB/(B-1))/(L/(B-1))

 

to the answer.

Cancel out the things that would cancel if you inverted and

multiplied.

 

 

and the only thing that is left is the B in the top.

 

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