Question

Please help me on this

Answer 1

Answer: Option a.

Explanation:

To rationalize the expression you need to:

Multiply the numerator and the denominator by the conjugate of the denominator.

The conjugate of the denominator is:
`√(x)-√(7)`

Remember that:

`(\sqrt[n]{x})^n=x\\\\(\sqrt[n]{x})(\sqrt[n]{y})=\sqrt[n]{xy}`

Therefore, multiplying the numerator and the denominator by the conjugate of the denominator (
`√(x)-√(7)`), you get:

`=((√(x))(√(x)-√(7)))/((√(x)+√(7))(√(x)-√(7)))\\\\=((√(x))^2-(√(x))(√(7)))/((√(x))^2-(√(7))^2)\\\\=(x-√(7x))/(x-7)`

This is the option a.