Step-by-step explanation:

a , b are rational numbers

try to understand the answer given

Verified answer

Answer:

Question:-

[tex] \frac{ \sqrt{7} + \sqrt{3} }{2 \sqrt{7} - 3 \sqrt{3} } = a - b \sqrt{21} .[/tex]

Solution:-

By rationalising the denominator, we get,

[tex] \frac{ \sqrt{7} + \sqrt{3} }{2 \sqrt{7} - 3 \sqrt{3} } \times \frac{2 \sqrt{7} + 3 \sqrt{3} }{2 \sqrt{} + 3 \sqrt{3} } . \\ = \frac{( \sqrt{7)} (2 \sqrt{7} ) + (3 \sqrt{3} )( \sqrt{7} ) + ( 2\sqrt{7})( \sqrt{3} ) + ( \sqrt{3})(3 \sqrt{3} ) }{(2 \sqrt{7} ) {}^{2} - (3 \sqrt{3}) {}^{2} } . \\ = \frac{11 + 3 \sqrt{21} + 2 \sqrt{21} + 9 }{28 - 27} . \\ = \frac{23 + 5 \sqrt{21} }{1} . \\ = 23 + 5 \sqrt{21} . \\ [/tex]

Hence, a = 23 and b = 5 .