Answer:
[tex]\frac{1-\sqrt{7} }{2}[/tex]
Step-by-step explanation:
given [tex]\frac{5-2\sqrt{7} }{3-\sqrt{7} }[/tex]
To rationalise the denominator multiply the numerator/ denominator by the conjugate of the denominator.
the conjugate of 3 - [tex]\sqrt{7}[/tex] is 3 + [tex]\sqrt{7}[/tex], hence
[tex]\frac{5-2\sqrt{7} }{3-\sqrt{7} }[/tex] × [tex]\frac{3+\sqrt{7} }{3+\sqrt{7} }[/tex]
= (15 + 5[tex]\sqrt{7}[/tex] - 6[tex]\sqrt{7}[/tex] - 14 ) / (9 - 7)
= [tex]\frac{1-\sqrt{7} }{2}[/tex] ← in simplified radical form
