Question

Which choice is equivalent to the fraction below when x is an appropriate value? 4/4-sqrt(6x)

Answer 1

Answer: Choice C)
`(8+2√(6x))/(8-3x)`

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Work Shown:

`y = (4)/(4-√(6x))\\\\y = (4(4+√(6x)))/((4-√(6x))(4+√(6x)))\\\\y = (4(4+√(6x)))/(4^2 - (√(6x))^2)\\\\y = (4(4+√(6x)))/(16-6x)\\\\y = (2*2(4+√(6x)))/(2(8-3x))\\\\y = (2(4+√(6x)))/(8-3x)\\\\y = (8+2√(6x))/(8-3x)\\\\`

This shows why choice C is the answer.

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Notes:

• If you have a+sqrt(b) in the denominator, multiply top and bottom by a-sqrt(b) which is the conjugate, and that will rationalize the denominator.
• In the second step, I multiplied top and bottom by 4+sqrt(6x) to rationalize the denominator
• In step 3, I used the difference of squares rule. In the step afterward, the square root is eliminated.