Question

Which choice is equivalent to the quotient shown here for acceptable values of x?

Answer 1

C √(5/(x-1))

Explanation:

You want the simplified quotient √(25(x-1)) ÷ √(5(x -1)²).

Simplification

The quotient is simplified by cancelling common factors from numerator and denominator.

`(√(25(x-1)))/(√(5(x-1)^2))=\sqrt{(25(x-1))/(5(x-1)^2)}=\sqrt{(5\cdot5(x-1))/((x-1)\cdot(5(x-1))}=\boxed{\sqrt{(5)/(x-1)}}`

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Additional comment

The radicand must be positive, so the domain is x > 1.

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