Write
2x - 3
-------- - 3x
2x - 1
as a rational expression.
===================================
2x - 3
-------- - 3x
2x - 1
Put the 3x over 1
2x - 3 3x
-------- - ----
2x - 1 1
The LCD is (2x - 1)
The first fraction already has the LCD so
don't need to multiply it by anything,
The second fraction needs to have the
LCD for its denominator, so we multiply
top and bottom by (2x - 1)
2x - 3 3x(2x - 1)
-------- - ------------
2x - 1 1(2x - 1)
Distribute to remove the parentheses:
2x - 3 6x² - 3x
-------- - ----------
2x - 1 2x - 1
Write as one fraction over the common
denominator.
Caution: the - sign in
front of the second fraction causes
BOTH signs in its numerator to change,
so be sure to change the sign of the
"- 3x" to "+ 3x":
2x - 3 - 6x² + 3x
-------------------
2x - 1
Combine the 2x and the 3x as 5x
5x - 3 - 6x²
--------------
2x - 1
You can stop there, or if your
teacher wants you to, you can
rearrange the numerator in
descending order of exponents
of x:
-6x² + 5x - 5
---------------
2x - 1
The numerator will not factor.
However, in other similar problems
it sometimes will, and when it
does, sometimes a factor of it will
cancel with a factor in the
denominator. That's why your
teacher may require you to arrange
it in descending order, because
that will be necessary in other
similar problems in which the
numerator factors.
Edwin