HP 40gs User Manual page 195

hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM
PARTFRAC
QUOTE
Computer Algebra System (CAS)
In real mode, the result is:
2 2
( 2 x ⋅ ) ⋅ (
x + + 1 x
In complex mode (using CFG), the result is:
1
⋅ ( ( ) ⋅ ) ⋅
----- -
2x + 1 + i 2
16
⋅ ( ( ) ⋅ )
2x 1 i – – 2
Partial fraction expansion
PARTFRAC has a rational fraction as an argument.
PARTFRAC returns the partial fraction decomposition of
this rational fraction.
Example
To perform a partial fraction decomposition of a rational
function, such as:
5
x
------------------------------------------------------------------------ -
4 3
⋅
x – 2 x +
you use the PARTFRAC command.
In real and direct mode, this produces:
--------------------- -
x + + 2
⋅
2 x
In complex mode, this produces:
1 3i –
------------- -
4
------------- -
x + + 2
x +
Quoted expression
QUOTE(expression) is used to prevent an expression
from being evaluated or simplified.
Example 1
Typing:
⎛
( (
im QUOTE 2X 1 –
⎝
gives:
+∞
2 x ⋅ )
– + 1
( ( ) ⋅ ) ⋅ ( (
2x 1 – + i 2 2x +
3
⋅
– 2 x + 1
2
⋅ ( ⋅ )
2 x – 2 x + 1
x 3 – 1 –
------------------ -
+
2 x ⋅ 2
2 –
+ 2
1 – 1 + 3i
----- - ------------- -
2 4
---------- - ------------- -
+ +
i x 1 – x i –
1
) ⋅ -- - 1 ) ,
EXP( – X = +∞
X
) ⋅ )
1 i – 2
⎞
⎠
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