Simplify. Rationalize the denominato $$ \frac{10}{-5-\sqrt{15}} $$

Question

UpStudy AI · Accepted Answer

To simplify and rationalize the denominator for the expression 10/(-5 - √15), follow these steps:

1. Multiply the numerator and denominator by the conjugate of the denominator. The conjugate of (–5 – √15) is (–5 + √15).

10/(-5 - √15) = [10(–5 + √15)] / [(-5 - √15)(–5 + √15)]

2. Multiply out the denominator using the difference of squares:

(-5 - √15)(–5 + √15) = (-5)² - (√15)² = 25 - 15 = 10

3. Substitute the simplified denominator back into the expression:

[10(–5 + √15)] / 10

4. Simplify by canceling the common factor of 10:

= –5 + √15

Thus, the simplified and rationalized form of the expression is:

√15 – 5
The simplified and rationalized form of the expression is $$ \sqrt{15} - 5 $$.

Simplify. Rationalize the denominato