2018 · Q18
What is the value of (√5 - √3)/(√5 + √3) - (√5 + √3)/(√5 - √3)?
Elementary MathematicsNumber System
- A-2√15
- B2√15
- C√15
- D-√15
Explanation
Use the common denominator (√5)² − (√3)² = 2: the difference equals [(√5−√3)² − (√5+√3)²]/2 = [(8 − 2√15) − (8 + 2√15)]/2 = −2√15. The keyed answer is (A). Note the minus sign applies to the entire second fraction.