HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 195
Example, Example 1
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hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM PARTFRAC QUOTE In real mode, the result is: (x2 + 2 ⋅ x + 1) ⋅ (x2 - 2 ⋅ x + 1) In complex mode (using CFG), the result is: --1--- ⋅ (2x + (1 + i) ⋅ 2) ⋅ (2x-(1 + i) ⋅ 2) ⋅ (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: x--5----------2----⋅---x---3----+-----1 x4 - 2 ⋅ x3 + 2 ⋅ x2 - (2 ⋅ x + 1) you use the PARTFRAC command. In real and direct mode, this produces: x + 2 + ------x---------3------2 ⋅ x2 + 2 + -2----⋅----x--1--------2- In complex mode, this produces: 1----------3----i -----1- 1-----+-----3---i x + 2 + ------4 2 4-------x+i x-1 x-i Quoted expression QUOTE(expression) is used to prevent an expression from being evaluated or simplified. Example 1 Typing: i m ⎛⎝ Q U O T E ( ( 2 X - 1) ⋅ E X P ( -1-X - 1 ), X = +∞⎠⎞ gives: +∞ Computer Algebra System (CAS) 14-13