Divide Square Roots: example 9.73

Simplify: $\frac{\sqrt{x} + \sqrt{7}}{\sqrt{x} - \sqrt{7}}$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify: $\frac{\sqrt{p} + \sqrt{2}}{\sqrt{p} - \sqrt{2}}$ .

How did it go?


Multiply the numerator and denominator by the conjugate of the denominator.
Multiply the conjugates in the denominator.
Simplify the denominator.
We do not square the numerator. In factored form, we can see there are no common factors to remove from the numerator and denominator.


Multiply the numerator and denominator by the conjugate of the denominator.
Multiply the conjugates in the denominator.
Simplify the denominator.
We do not square the numerator. In factored form, we can see there are no common factors to remove from the numerator and denominator.