(i) The given expression is
Assumeand
. Then the given expression can be rewritten as
Recall the formula for sum of two cubes
Using the above formula, the expression becomes
Note that both and b are positive. So, neither
nor any factor of it can be zero.
Therefore we can cancel the termfrom both numerator and denominator. Then the expression becomes
(ii) The given expression is
Assumeand
. Then the given expression can be rewritten as
Recall the formula for difference of two cubes
Using the above formula, the expression becomes
Note that both, b is positive and unequal. So, neither
nor any factor of it can be zero.
Therefore we can cancel the termfrom both numerator and denominator. Then the expression becomes
(iii) The given expression is
Assumeand
. Then the given expression can be rewritten as
Recall the formula for difference of two cubes
Using the above formula, the expression becomes
Note that both, b is positive and unequal. So, neither
nor any factor of it can be zero.
Therefore we can cancel the termfrom both numerator and denominator. Then the expression becomes