3.
1. Write the expression as a simplified rational expression. Show your work.
14x+4
-----------
2 1
----- + -----
3x 2x+1
Easiest to simplify the denominator, firtst
2 ( 2x + 1) + 1 ( 3x) 4x + 2 + 3x 7x + 2
__________________ = ___________ = __________
3x (2x + 1) 3x (2x + 1) 3x (2x + 1)
And the numerator simplifies to 2 ( 7x + 2)
So we have
2 ( 7x + 2)
____________________ invert the denominator and multiply
(7x + 2) / [3x (2x + 1) ]
2 ( 7x + 2) [ 3x ( 2x + 1) ]
______________________ = 2 [ 3x ( 2x + 1) ] = 2 [ 6x^2 + 3x] = 12x^2 + 6x
(7x + 2)