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

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

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

$$\frac{b^{1/4}{c}^{1/2}-c^{1/4}{b}^{1/2}}{b^{1/4}{c}^{1/2}-c^{1/4}}$$$$\frac{b^{1/4}{c}^{1/4}(c^{1/4}-b^{1/4})}{c^{1/4}(b^{1/4}{c}^{1/4}-1)}$$$$\frac{b^{1/4}(c^{1/4}-b^{1/4})}{b^{1/4}{c}^{1/4}-1}$$$$\frac{b^{1/4}(c^{1/4}-b^{1/4})}{b^{1/4}{c}^{1/4}-1}\cdot \frac{b^{1/4}{c}^{1/4}+1}{b^{1/4}{c}^{1/4}+1}$$$$\frac{b^{1/4}(c^{1/4}-b^{1/4})(b^{1/4}{c}^{1/4}+1)}{b^{1/2}{c}^{1/2}-1}$$$$\frac{b^{1/4}(c^{1/4}-b^{1/4})(b^{1/4}{c}^{1/4}+1)}{b^{1/2}{c}^{1/2}-1}\cdot \frac{b^{1/2}{c}^{1/2}+1}{b^{1/2}{c}^{1/2}+1}$$$$\frac{b^{1/4}(c^{1/4}-b^{1/4})(b^{1/4}{c}^{1/4}+1)(b^{1/2}{c}^{1/2}+1)}{bc-1}$$

Commented by hardmath last updated on 28/May/24

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

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