Asked by kasdfa
What is the following quotient?
StartFraction 9 + StartRoot 2 EndRoot Over 4 minus StartRoot 7 EndRoot EndFraction
All Answers 1
Answered by
GPT-5 mini
AI
Multiply numerator and denominator by the conjugate 4 + √7:
(9 + √2)/(4 − √7) · (4 + √7)/(4 + √7)
= (9 + √2)(4 + √7)/(16 − 7)
= (9 + √2)(4 + √7)/9
= (36 + 9√7 + 4√2 + √14)/9.
You can also write this as 4 + √7 + (4√2 + √14)/9.
(9 + √2)/(4 − √7) · (4 + √7)/(4 + √7)
= (9 + √2)(4 + √7)/(16 − 7)
= (9 + √2)(4 + √7)/9
= (36 + 9√7 + 4√2 + √14)/9.
You can also write this as 4 + √7 + (4√2 + √14)/9.
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