Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Express the following rational function in continued-fraction form: $${4x^2+3x-7\over 2x^3+x^2-x+5}$$ The answer is : $${4 \over 2x- \frac{1}{2}} + { \frac{23}{8} \over x-\frac{63}{92}}-{\frac{406}{529} \over x+\frac{33}{23}}\tag{inline continued fraction}$$ which means $$ \cfrac{4}{2x- \frac{1}{2}+\cfrac{\frac{23}{8}}{x-\frac{63}{92}-\cfrac{\frac{406}{529}}{x+\frac{33}{23}}}} $$

share|cite|improve this question

1 Answer 1

up vote 4 down vote accepted

Here is the solution using integer coefficients $$ \begin{align} \cfrac{4x^2+3x-7}{2x^3+x^2-x+5} &=\cfrac1{\cfrac{2x^3+x^2-x+5}{4x^2+3x-7}}\\ &=\cfrac{8}{4x-1+\cfrac{23x+33}{4x^2+3x-7}}\\ &=\cfrac{8}{4x-1+\cfrac{529}{92x-63-\cfrac{1624}{23x+33}}}\\ \end{align} $$ The book's answer can be shown to be equal by cancelling fractions.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.