Question
Simplify: (√5 + √3)/(√5 − √3) + (√5 − √3)/(√5 + √3)
Solution
Let a = √5, b = √3. Expression = (a + b)/(a − b) + (a − b)/(a + b) = [(a + b)² + (a − b)²] / (a² − b²) (a + b)² = a² + 2ab + b² (a − b)² = a² − 2ab + b² Sum = 2a² + 2b² Denominator = a² − b² So expression = 2(a² + b²)/(a² − b²) Now a² = 5, b² = 3: = 2(5 + 3)/(5 − 3) = 2×8/2 = 8.
More Simplification Questions
- What value should come in the place of (?) in the following questions? 30% of 160 – 25% of 240 + 43 = ?
- Evaluate: √729 + √49 - √16 + 1/√64
- Determine the value of ‘p’ if p% of 600 + {1440 ÷ p of 16} × 8 = 156
- What value should come in place of (?) question mark in the given expression. 540 ÷ 9 ÷ 3 + 8 × 11 = ?
- 17% of 250 + ? = 108
- 26 X √25 + 15 - 80% of 120 = ?2
- What will come in the place of question mark (?) in the given expression? (√1089 + 84 ÷ 2) % of 348 = 416 - ?
- What will come in the place of question mark (?) in the given expression? (24 2 – 16 2 ) + 75% of 40% of 480 = ?
- What will come in place of (?), in the given expression. (28 × 4) + (96 ÷ 4) – 25 = ?
- If 960 ÷ 16 + 875 ÷ 25 - x + 28 × 6 = 1350 ÷ 18 × 222 ÷ 37, then the value of x is:
