Question

[Thế Quang]

chứng minh 3/(√6-√3)+4/(√7+√3) -1/(√7-√6) bằng 0

Answer 1

[Trần Thanh Phương]

\(\frac{3}{\sqrt{6}-\sqrt{3}}+\frac{4}{\sqrt{7}+\sqrt{3}}-\frac{1}{\sqrt{7}-\sqrt{6}}\)

\(=\frac{3\left(\sqrt{6}+\sqrt{3}\right)}{\left(\sqrt{6}-\sqrt{3}\right)\left(\sqrt{6}+\sqrt{3}\right)}+\frac{4\left(\sqrt{7}-\sqrt{3}\right)}{\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)}-\frac{\sqrt{7}+\sqrt{6}}{\left(\sqrt{7}+\sqrt{6}\right)\left(\sqrt{7}-\sqrt{6}\right)}\)

\(=\frac{3\left(\sqrt{6}+\sqrt{3}\right)}{6-3}+\frac{4\left(\sqrt{7}-\sqrt{3}\right)}{7-3}-\frac{\sqrt{7}+\sqrt{6}}{7-6}\)

\(=\sqrt{6}+\sqrt{3}+\sqrt{7}-\sqrt{3}-\sqrt{7}-\sqrt{6}\)

\(=0\)( đpcm )