Final answer:
To simplify the expression √5 - √3 ÷ √5 + √3, we need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator. The simplified expression is 2, and the values of a and b in the expression a - b√15 are 2 and 0, respectively. Therefore, a + b = 2.
Step-by-step explanation:
To simplify the expression √5 - √3 ÷ √5 + √3, we need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of √5 + √3 is √5 - √3. This gives us:
(√5 - √3)(√5 - √3) - √3(√5 - √3) ÷ (√5 + √3)(√5 - √3)
Simplifying further, we get √5 x √5 - √5 x √3 - √3 x √5 + √3 x √3 - √3 x √5 + √3 x √3 ÷ √5 x √5 - √5 x √3 + √3 x √5 - √3 x √3.
Notice that the middle terms will cancel out since they have opposite signs. We will also be left with √5 x √5 - √3 x √3, which simplifies to 5 - 3, or 2. Therefore, the simplified expression is 2.
The values of a and b in the expression a - b√15 are 2 and 0, respectively. Hence, a + b = 2 + 0 = 2.