3 2
----- - ------
2a -2 1 - a
5 3
----- - ------
2x - 4 2 - x
need a little understanding on these anyone?
I don't understand the second term. Is it this?
3 2
----- - ------ =
2a -2 1 - a
3 2
----- - ------ =
2(a -1) 1 - a
3 2
----- - ------ =
2(a -1) -( a-1)
3 2 3/2 +2
----- + ------ = -----------------
2(a -1) (a-1) (a-1)
4.5/(a-1)
Same principles on the second, get a common denominator.
oops, type, that is a 3.5 in the numerator.
Let's break down the first expression:
3 2
----- - ------
2a -2 1 - a
To simplify this expression, we need to find a common denominator for the two terms. The denominators are 2a - 2 and 1 - a. The LCM (Least Common Multiple) of these two denominators is 2(a - 1).
Now, let's rewrite the expression with the common denominator:
3 * (1 - a)
------------ - 2
2(a -1)
Now let's simplify further by applying the distributive property:
3 - 3a
------- - 2
2(a -1)
To combine the terms, we need to multiply the numerators and denominators:
(3 - 3a) - 2(1 - a)
---------------------
2(a - 1)
Now distribute the -2:
3 - 3a - 2 + 2a
------------------
2(a - 1)
Combine like terms:
-3a + 2a + 3 - 2
---------------
2(a - 1)
Simplify:
-a + 1
-------
(a - 1)
So the simplified expression is (-a + 1) / (a - 1).
Now let's move on to the second expression:
5 3
----- - ------
2x - 4 2 - x
Following the same steps as above, we need to find a common denominator. The denominators are 2x - 4 and 2 - x. The LCM of these two denominators is 2 - x.
Rewriting the expression with the common denominator:
5 * (2 - x)
--------------
2x - 4
Apply the distributive property:
10 - 5x
--------------
2x - 4
No further simplification is necessary for this expression.