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MATH / Two nonzero real numbers a and b satisfy ab=a−b. Find all possible values of (a)/(b)+(b)/(a)−ab. Enter all possible values, separated by commas.

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problem

Two nonzero real numbers aa and bb satisfy ab=a−b.ab = a - b. Find all possible values of ab+ba−ab.\frac {a}{b} + \frac {b}{a} - ab. Enter all possible values, separated by commas.
Plain-text mathematical notation (without MathML)
Two nonzero real numbers a and b satisfy ab=a−b. Find all possible values of (a)/(b)+(b)/(a)−ab.

Enter all possible values, separated by commas.
Original LaTeX notation
Two nonzero real numbers $a$ and $b$ satisfy $ab = a - b.$ Find all possible values of $\frac {a}{b} + \frac {b}{a} - ab.$

Enter all possible values, separated by commas.

level

Level 2

type

Intermediate Algebra

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Source and history

task_id
76c5a92d-32b8-56fa-ad9f-687579abb0b5
task_key
intermediate~5falgebra--test--76c5a92d-32b8-56fa-ad9f-687579abb0b5
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import