(((1)/(x)-(2)/(3))/(9-6x))/(9x^(2)+12x)

Question

I need help 

Answer 1

Take it piece by piece.

 

Step 1 - The first part is (1/x)-(2/3).  You have to get common denominators.  Multiply each term by (3x)/(3x).  This will give you the result of (3-2x)/(3x).

 

Step 2 - Divide that by (9-6x) which actually factors to (3)(3-2x).  Make that portion a fraction [3(3-2x)]/1.  Now you're dividing a fraction by a fraction.  That's "bad", so you multiply by the reciprocal.   [(3-2x)/(3x)]*[1/(3(3-2x))].  The (3-2x) cancels.  This gives the result of 1/(9x).

 

Step 3 - Divide this by (9x²+12x).  Again, make the denominator a fraction, and then multiply by the reciprocal.  This will give a final result of 1/(81x³+108x²).  Or, if you want those factored, you would have 1/[27x²(3x+4)]