Question

Evaluate the expression 1/(x-2) when x = 3√2.

Answer 1

To evaluate the expression 1/(x-2) when x = 3√2, substitute the value of x into the expression and simplify the denominator. The value of 1/(x-2) when x = 3√2 is √2/2.

Step-by-step explanation:

To evaluate the expression 1/(x-2) when x = 3√2, we substitute the value of x into the expression. Here's the step-by-step calculation:

1. Substitute x = 3√2 into the expression: 1/(3√2 - 2).
2. Simplify the denominator by subtracting 2 from 3√2: 3√2 - 2 = 3√2 - 2√2 = √2.
3. Now we have 1/√2.
4. Rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator: √2/√2 * √2/√2 = √2/2.

Therefore, the value of 1/(x-2) when x = 3√2 is √2/2.