Final answer:
To rationalize the denominator and simplify the fraction √8/√2 - √2, we need to multiply both the numerator and denominator by the conjugate of the denominator. This results in the equivalent fraction (4 + 2√2) / (2 - √2).
Step-by-step explanation:
To solve this problem, we need to rationalize the denominator and simplify the fraction. We can do this by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of √2 - √2 is √2 + √2. When we multiply them, we get:
√8(√2 + √2) / (√2 - √2)(√2 + √2)
Simplifying the numerator: √8(√2 + √2) = √8 x √2 + √8 x √2 = √16 + √8 = 4 + 2√2
Simplifying the denominator: (√2 - √2)(√2 + √2) = √4 - √2 = 2 - √2
Putting it all together:
√8(√2 + √2) / (√2 - √2)(√2 + √2) = (4 + 2√2) / (2 - √2)