Question

Please help me on this

Answer 1

Answer: Option a.

Step-by-step 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: $\sqrt{x}-\sqrt{7}$

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 ($\sqrt{x}-\sqrt{7}$), you get:

$=\frac{(\sqrt{x})(\sqrt{x}-\sqrt{7})}{(\sqrt{x}+\sqrt{7})(\sqrt{x}-\sqrt{7})}\\\\=\frac{(\sqrt{x})^2-(\sqrt{x})(\sqrt{7})}{(\sqrt{x})^2-(\sqrt{7})^2}\\\\=\frac{x-\sqrt{7x}}{x-7}$

This is the option a.