what rational expression divided by 3a over 4 equals 1 over three

Let the rational expression be R

Then R divided by 3a over 4 equals 1 over three

      ÷  = 
          
Put the R over 1

      ÷  = 

Invert the  and change the ÷ to ×

      ×  = 

Multiply numerators and denominators on the left:

      = 

Multiply both sides by the LCD, 

      = 

The 's cancel on the left, leaving just 
The 's cancel on the right, leaving just .

           = 

Divide both sides by 4:

          =

That's the rational expression.

Let's check and see:

      ÷  = 

    ÷  = 

Invert the second fraction on the left and change the ÷ to ×:

    ×  = 

The 's  and the 's cancel on the left, leaving 
just 

                   = 

So it checks.

Edwin