Basically, a rational expression would include only additions, subtractions, multiplications, divisions, and integer powers, while an irrational expression could, in addition, include several additional functions, such as roots (or equivalently, non-integer powers), exponential functions, logarithms, trigonometric functions, and just about any other function.
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what are the example of quotient orf rational algebraic expression.
Lcd/lcm
cvxbgfhbfdh
A collection of more than one term.
By long division. Factorisation may work but you cannot depend on that.