Multiply or divide as indicated

a.    (5x+5)/6   multiplied by  3x/(x²+x)
                                       
 5x + 5       3x
 ------ · ---------  
    6       x² + x

Factor 5x + 5 as 5(x + 1)
Factor x² + x as x(x + 1)

 5(x + 1)      3x
 -------- · ---------  
    6       x(x + 1)


Multiply numerators and denominators. Do not remove the
parentheses, though:

  15x(x + 1)     
 ------------  
  6x(x + 1)

15 and 6 can both be divided by 3

  5
  15x(x + 1)     
 ------------  
  6x(x + 1)
  2

We can also cancel the x's and the (x + 1)'s:

  5    1
  15x(x + 1)     
 ------------  
  6x(x + 1)
  2    1

Answer is simply:

     5
    ---
     2

========================================

b.    (x²+x)/10   divided by  (2x+4)/5

 x² + x     2x + 4
 ------ ÷ ---------  
   10         5

To divide, invert the second and multiply

 x² + x       5
 ------ · ---------  
   10       2x + 4

Factor x² + x as x(x + 1)
Factor 2x + 4 as 2(x + 2)

 x(x + 1)      5
 -------- · ---------  
    10       2(x + 2)

Multiply numerators and denominators. Do not remove the
parentheses, though:

   5x(x + 1)     
 ------------  
   20(x + 2)

Cancel the 5 into the 20
   
   1
   5x(x + 1)     
 ------------  
   20(x + 2)
    4

That's the only thing that will cancel, so the
answer is

  
   x(x + 1)     
 ------------  
   4(x + 2)
    
You can leave the answer like that, or, if you
want to, you can remove the parentheses and get

   x² + x
  --------
   4x + 8

Edwin