Question

(√17-√8)(√17+√8)/(√8+√5)(√5-√8)

Answer 1

(√17-√8)(√17+√8)/(√8+√5)(√5-√8)=(17-8):(5-8)=9:(-3)=-3

Answer 2

To simplify the given expression, we can use the difference of squares formula, which states that (a^2 - b^2) can be factored as (a + b)(a - b). Let's apply this formula step by step to the expression:

Expression: (√17 - √8)(√17 + √8) / (√8 + √5)(√5 - √8)

Step 1: Apply the difference of squares formula to the numerator: (√17 - √8)(√17 + √8) = (√17)^2 - (√8)^2 = 17 - 8 = 9

Step 2: Apply the difference of squares formula to the denominator: (√8 + √5)(√5 - √8) = (√5)^2 - (√8)^2 = 5 - 8 = -3

Now, the expression becomes: 9 / (-3)

Step 3: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD is 3.

9 / (-3) = 3 / (-1)

The simplified expression is 3 / (-1), which is equal to -3.

Therefore, (√17 - √8)(√17 + √8) / (√8 + √5)(√5 - √8) simplifies to -3.