Question

2 over(x+1/x)over 2 =10-x-1/x is what!?

Answer 1

simplifying the expression within the numerator: 2 over (x + 1/x).

To simplify this part, we need to find the least common denominator (LCD) of (x + 1/x). The LCD is x, since x and 1/x already have a common factor of 1. Multiplying the numerator and denominator by x, we get: 2x over (x^2 + 1).

2. Next, let's simplify the expression within the denominator: 2.

Since there are no variables involved, the denominator remains the same.

3. Now, we can rewrite the entire expression as: (2x over (x^2 + 1)) over 2.

4. To simplify this further, we can multiply the numerator by the reciprocal of the denominator.

The reciprocal of 2 is 1/2. So, we have: (2x over (x^2 + 1)) times (1/2).

5. Multiplying the numerators together and the denominators together, we get: 2x over 2(x^2 + 1).

6. Now, we can cancel out the common factor of 2 in the numerator and the denominator: 2x over x^2 + 1.

7. Finally, we have the simplified expression: 2x over x^2 + 1.

Therefore, the simplified form of the given expression 2 over (x + 1/x) over 2 is 2x over x^2 + 1.

Help from the AI

Answer 2

1. Start with the equation: 2/(x + 1/x) = 10 - x - 1/x.

2. Multiply both sides of the equation by (x + 1/x) to get rid of the fraction on the left side:

2 = (10x - x^2 - 1).

3. Rearrange the terms and set the equation equal to zero:

x^2 - 10x + 1 = 0.

4. You can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a).

In this case, a = 1, b = -10, and c = 1.

x = (10 ± √((-10)^2 - 4(1)(1))) / (2(1)).

5. Calculate the values of x:

x = (10 ± √(100 - 4)) / 2,

x = (10 ± √96) / 2,

x = (10 ± 4√6) / 2.

6. Simplify further:

x = 5 ± 2√6.

So, the solutions to the equation are x = 5 + 2√6 and x = 5 - 2√6.