[tex] \frac{9+\sqrt{2}}{4-\sqrt{7}} [/tex]
multiply by the conjugate of denominator.
[tex] =\frac{9+\sqrt{2}}{4-\sqrt{7}}* \frac{4+\sqrt{7}}{4+\sqrt{7}} [/tex]
[tex] =\frac{(9+\sqrt{2})(4+\sqrt{7})}{(4-\sqrt{7})(4+\sqrt{7})} [/tex]
apply formula (a+b)(a-b)=a^2-b^2
[tex] =\frac{(9+\sqrt{2})(4+\sqrt{7})}{(4^2-(\sqrt{7})^2)} [/tex]
[tex] =\frac{(9+\sqrt{2})(4+\sqrt{7})}{16-7} [/tex]
[tex] =\frac{(9+\sqrt{2})(4+\sqrt{7})}{9} [/tex]
[tex] =\frac{36+9 \sqrt{7} +4 \sqrt{2} + \sqrt{14}}{9} [/tex]
Hence final answer is [tex] \frac{36+9 \sqrt{7} +4 \sqrt{2} + \sqrt{14}}{9} [/tex]
