Express the following rational function in continued-fraction form: <mrow class="MJX-TeXAtom-OR

Jordon Haley

Jordon Haley

Answered question

2022-05-15

Express the following rational function in continued-fraction form:
4 x 2 + 3 x 7 2 x 3 + x 2 x + 5
The answer is :
(inline continued fraction) 4 2 x 1 2 + 23 8 x 63 92 406 529 x + 33 23
which means
4 2 x 1 2 + 23 8 x 63 92 406 529 x + 33 23

Answer & Explanation

Lucille Melton

Lucille Melton

Beginner2022-05-16Added 18 answers

Here is the solution using integer coefficients
4 x 2 + 3 x 7 2 x 3 + x 2 x + 5 = 1 2 x 3 + x 2 x + 5 4 x 2 + 3 x 7 = 8 4 x 1 + 23 x + 33 4 x 2 + 3 x 7 = 8 4 x 1 + 529 92 x 63 1624 23 x + 33
The book's answer can be shown to be equal by cancelling fractions.

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