evaluate 2/2root 2+3 /root 2/2root 2-3

Answer 1

To evaluate the given expression, let's simplify each part step by step.

1) Simplifying the numerator: 2 / (2√2)
To simplify this, multiply the numerator and denominator by the conjugate of the denominator, which is √2.
(2 / (2√2)) * (√2 / √2) = (2√2) / (2*√2*√2) = (2√2) / (2√4) = (2√2) / (2*2) = √2 / 2

2) Simplifying the denominator: √2 / (2√2 - 3)
We can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is (2√2 + 3).
(√2 / (2√2 - 3)) * ((2√2 + 3) / (2√2 + 3)) = (√2 * (2√2 + 3)) / ((2√2 - 3) * (2√2 + 3)) = (2√4 + 3√2) / (4*2 - 3*3) = (2√4 + 3√2) / (8 - 9) = (2√4 + 3√2) / (-1) = -(2√4 + 3√2)

Now, we can substitute the simplified numerator and denominator back into the original expression:

(√2 / 2) / (-(2√4 + 3√2))

We cannot simplify this any further since the numerator and denominator do not share any common factors. Therefore, the evaluated expression is (√2 / 2) / (-(2√4 + 3√2)).