Simplify-b-1-4-c-c-1-4-b-b-1-4-c-c-1-4-

Question Number 207771 by hardmath last updated on 25/May/24

$$\mathrm{Simplify}:\:\:\:\:\:\frac{\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{b}}}\:\:\sqrt{\boldsymbol{\mathrm{c}}}\:\:−\:\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{c}}}\:\:\sqrt{\boldsymbol{\mathrm{b}}}}{\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{b}}}\:\:\sqrt{\boldsymbol{\mathrm{c}}}\:\:−\:\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{c}}}}\:\:=\:\:? \\ $$

Answered by Rasheed.Sindhi last updated on 26/May/24

$$\frac{{b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{2}} −{c}^{\mathrm{1}/\mathrm{4}} {b}^{\mathrm{1}/\mathrm{2}} }{{b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{2}} −{c}^{\mathrm{1}/\mathrm{4}} } \\ $$$$\frac{{b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{4}} \left({c}^{\mathrm{1}/\mathrm{4}} −{b}^{\mathrm{1}/\mathrm{4}} \right)}{{c}^{\mathrm{1}/\mathrm{4}} \left({b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{4}} −\mathrm{1}\right)} \\ $$$$\frac{{b}^{\mathrm{1}/\mathrm{4}} \left({c}^{\mathrm{1}/\mathrm{4}} −{b}^{\mathrm{1}/\mathrm{4}} \right)}{{b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{4}} −\mathrm{1}} \\ $$$$\frac{{b}^{\mathrm{1}/\mathrm{4}} \left({c}^{\mathrm{1}/\mathrm{4}} −{b}^{\mathrm{1}/\mathrm{4}} \right)}{{b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{4}} −\mathrm{1}}\centerdot\frac{{b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{4}} +\mathrm{1}}{{b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{4}} +\mathrm{1}} \\ $$$$\frac{{b}^{\mathrm{1}/\mathrm{4}} \left({c}^{\mathrm{1}/\mathrm{4}} −{b}^{\mathrm{1}/\mathrm{4}} \right)\left({b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{4}} +\mathrm{1}\right)}{{b}^{\mathrm{1}/\mathrm{2}} {c}^{\mathrm{1}/\mathrm{2}} −\mathrm{1}} \\ $$$$\frac{{b}^{\mathrm{1}/\mathrm{4}} \left({c}^{\mathrm{1}/\mathrm{4}} −{b}^{\mathrm{1}/\mathrm{4}} \right)\left({b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{4}} +\mathrm{1}\right)}{{b}^{\mathrm{1}/\mathrm{2}} {c}^{\mathrm{1}/\mathrm{2}} −\mathrm{1}}\centerdot\frac{{b}^{\mathrm{1}/\mathrm{2}} {c}^{\mathrm{1}/\mathrm{2}} +\mathrm{1}}{{b}^{\mathrm{1}/\mathrm{2}} {c}^{\mathrm{1}/\mathrm{2}} +\mathrm{1}} \\ $$$$\frac{{b}^{\mathrm{1}/\mathrm{4}} \left({c}^{\mathrm{1}/\mathrm{4}} −{b}^{\mathrm{1}/\mathrm{4}} \right)\left({b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{4}} +\mathrm{1}\right)\left({b}^{\mathrm{1}/\mathrm{2}} {c}^{\mathrm{1}/\mathrm{2}} +\mathrm{1}\right)}{{bc}−\mathrm{1}} \\ $$

Commented by hardmath last updated on 28/May/24

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{dear}\:\mathrm{professor} \\ $$

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