MODERATE EXERCISES - Symbol Manipulation
(4) Write each sum or difference as a single fraction.
(a) 32
- 32 - 32
---- ----
3 5
(b) - 20
--- ---
t t2
(c) 5k + x3
----
2k
(d) 14 + 9
-------- --------
(2x - 3) (2x + 3)
(e) 2 + 5 - 3
--- ------- -------
x x - 1 x2 - x
SOLUTION:
(a) 32 - 32 - 32
---- ----
3 5
=(15)32 - (5)32 - 32
---- ------- ----
(15) (5)3 5
= 32( 15 - 5 -1) 32(9)
-------------- = ------
15 15
= 32(3) 96
------- = ------
5 5
(b) - 20 (t) - 20
--- --- = ------ ----
t t2 (t)(t) t2
= (t) - 20
----------
t2
(c) 5k + x3 (2k)(5k) + x3
---- = -------- ----
2k 2k 2k
= 10k2 + x3
---------
2k
(d) 14 + 9 14(2x + 3) + 9(2x - 3) 28x + 42 + 18x - 27
-------- -------- = ------------------------ = -------------------
(2x - 3) (2x + 3) (2x - 3)(2x + 3) 4x2 + 6x - 6x - 9
= 46x + 15
----------
4x2 - 9
(e) 2 5 3 2(x - 1) 5x 3
- + ------- - ------- = ---------- + --------- - ----------
x x - 1 x2 - x x2 - x x2 - x x2 - x
7x - 5
= --------
x2 - x
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