Question

((x - 2)/(x + 2) - (x + 2)/(x - 2)) * (x ^ 2 - 4)/(4x)​

Answer 1

Ответ:

-1

Объяснение:

((x - 2)/(x + 2) - (x + 2)/(x - 2)) * (x ^ 2 - 4)/(4x)​ =

= ((х-2)² - (х+2)²)/(х²-4) * (х²-4)/4х = (х²-4х+4-х²-4х-4)/4х = -4х/4х = -1.

Answer 2

To simplify the given expression, let's break it down step by step:

Expression: ((x - 2)/(x + 2) - (x + 2)/(x - 2)) * (x^2 - 4)/(4x)

Step 1: Simplify the rational expressions inside the parentheses.

The expression can be rewritten as:

[(x - 2)/(x + 2)] - [(x + 2)/(x - 2)] * (x^2 - 4)/(4x)

Now, let's simplify each fraction separately:

First fraction: (x - 2)/(x + 2)

Second fraction: (x + 2)/(x - 2)

Step 2: Combine the fractions using a common denominator.

The common denominator for (x + 2) and (x - 2) is (x + 2)(x - 2). So, we can rewrite the expression as:

[(x - 2)(x - 2)/(x + 2)(x - 2)] - [(x + 2)(x + 2)/(x + 2)(x - 2)] * (x^2 - 4)/(4x)

Simplifying further:

[(x^2 - 4)/(x^2 - 4)] - [(x^2 + 4x + 4)/(x^2 - 4)] * (x^2 - 4)/(4x)

Step 3: Cancel out the common factors.

The expression becomes:

1 - (x^2 + 4x + 4)/(x^2 - 4) * (x^2 - 4)/(4x)

Step 4: Simplify the multiplication.

The (x^2 - 4) terms cancel out, leaving:

1 - (x^2 + 4x + 4)/(4x)

Step 5: Simplify further.

To simplify, let's factor the numerator:

1 - [(x + 2)(x + 2)]/(4x)

1 - (x + 2)^2/(4x)

Step 6: Distribute the negative sign.

1 - (x^2 + 4x + 4)/(4x)

Step 7: Combine like terms.

To subtract the fractions, we need a common denominator of 4x:

4x/4x - (x^2 + 4x + 4)/(4x)

(4x - x^2 - 4x - 4)/(4x)

(-x^2 - 4)/(4x)

Therefore, the simplified expression is (-x^2 - 4)/(4x).