Question

Which choice is equivalent to the fraction below when x is an appropriate

value? Hint: Rationalize the denominator and simplify

Sqrt(8)/sqrt(2)-sqrt(2)

Answer 1

To simplify the given fraction, you need to rationalize the denominator and simplify the expression.

Step-by-step explanation:

1. Rationalize the denominator of the fraction by multiplying the numerator and denominator by the conjugate of the denominator: sqrt(8)/sqrt(2)-sqrt(2) * sqrt(2)/sqrt(2) = (sqrt(8)*sqrt(2))/(sqrt(2)*sqrt(2)) - (sqrt(2)*sqrt(2))/(sqrt(2)*sqrt(2))
2. Simplify the expression by multiplying and simplifying the square roots: (sqrt(8)*sqrt(2))/(sqrt(2)*sqrt(2)) - (sqrt(2)*sqrt(2))/(sqrt(2)*sqrt(2)) = (sqrt(16))/(sqrt(4)) - 1
3. Continue simplifying the expression: (4)/(2) - 1 = 2 - 1 = 1

Answer 2

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)