The quotient of StartFraction 9 + StartRoot 2 EndRoot over 4 minus StartRoot 7 EndRoot EndFraction is (4 + √7) × (1 + √2)/ 9.
Given ( 9 + √2 )/ (4 - √7 ). Here, the numerator and denominators are radicals.
We rationalize the denominator by multiplying numerator and denominator with conjugate of the denominator, 4+√7.
(9 + √2)/ (4 - √7) × (4+√7)/ (4+√7)
= ((9 + √2) × (4+√7))/ ((4 - √7) × (4+√7))
= (36 + 9√7 + 4√2 + √14)/ (16 - 7)
= (36 + 9√7 + 4√2 + √14)/ 9
= 4 + √7 + √2(4 + √7)/ 9
= (4 + √7) × (1 + √2)/ 9
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