<PRE><B>Question 69233</B>
subtract
   4x + 1           -          3x - 2
-----------------   -      -----------------
25x^2 + 15x + 2     -       30x^2 + 11x + 1

-----------------------------------------------

Factor the denominators to get:

=[(4x+1)/(5x+2)(5x+1)]  -  [(3x-2)/(5x+1)(6x+1)]

Write each fraction over the least common denominator:
The least common denominator (lcd) is (5x+1)(5x+2)(6x+1)

=[(4x+1)(6x+1)/lcd] -[(3x-2)(5x+2)/lcd]

Combine the numerators and write the sum over the lcd:

=[24x^2+10x+1-(15x^2-4x-4)]/lcd

= (9x^2+14x+5)/lcd

Factor the numerator to get:

=[(9x+5)(x+1)] / [(5x+1)(5x+2)(6x+1)]

There are no factors common to numerator and denominator
so that is the final solution.

Cheers,
Stan H.</PRE>