If $straight x minus 1 over straight x equals 3 comma$ then find the value of $straight x cubed minus 1 over straight x cubed.$

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Solution

We know that

open parentheses straight x minus 1 over straight x close parentheses cubed equals x cubed minus 1 over x cubed minus 3 left parenthesis x right parenthesis open parentheses 1 over x close parentheses open parentheses x minus 1 over x close parentheses rightwards double arrow space open parentheses straight x minus 1 over straight x close parentheses cubed equals x cubed minus 1 over x cubed minus 3 open parentheses x minus 1 over x close parentheses rightwards double arrow space space space space left parenthesis 3 right parenthesis cubed equals x cubed minus 1 over x cubed minus 3 left parenthesis 3 right parenthesis rightwards double arrow x cubed minus 1 over x cubed space equals space 36

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