Question

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

Answer 1

Выходит такой ответ но вы всё таки проверьте

Answer 2

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

Expression: 2x / (x^2 - 4) - 2 / (x^2 - 4) : [(x + 1) / (2x - 2) - 1 / (x - 1)]

Step 1: Factor the denominators of the fractions. The denominators in both fractions are the same (x^2 - 4), which can be factored as (x + 2)(x - 2). Also, factor the denominator in the second part of the expression (2x - 2) as 2(x - 1).

Expression: 2x / [(x + 2)(x - 2)] - 2 / [(x + 2)(x - 2)] : [(x + 1) / {2(x - 1)} - 1 / (x - 1)]

Step 2: Find the common denominator for the fractions in the second part of the expression. The common denominator for (2(x - 1)) and (x - 1) is 2(x - 1).

Expression: 2x / [(x + 2)(x - 2)] - 2 / [(x + 2)(x - 2)] : [2(x + 1) / {2(x - 1)} - 2 / (2(x - 1))]

Step 3: Combine the fractions in the second part of the expression.

Expression: 2x / [(x + 2)(x - 2)] - 2 / [(x + 2)(x - 2)] : [(2(x + 1) - 2) / (2(x - 1))]

Step 4: Simplify the numerator in the second part of the expression.

Expression: 2x / [(x + 2)(x - 2)] - 2 / [(x + 2)(x - 2)] : [(2x + 2 - 2) / (2(x - 1))]

Expression: 2x / [(x + 2)(x - 2)] - 2 / [(x + 2)(x - 2)] : (2x / (2(x - 1)))

Step 5: Cancel out common factors between the numerator and denominator in the third part of the expression.

Expression: 2x / [(x + 2)(x - 2)] - 2 / [(x + 2)(x - 2)] : (x / (x - 1))

Step 6: Now, to combine the two fractions on the left side of the expression, find the common denominator, which is [(x + 2)(x - 2)].

Expression: [(2x - 2) - 2(x)] / [(x + 2)(x - 2)] : (x / (x - 1))

Step 7: Simplify the numerator on the left side of the expression.

Expression: (2x - 2 - 2x) / [(x + 2)(x - 2)] : (x / (x - 1))

Step 8: Further simplify the numerator on the left side.

Expression: (-2) / [(x + 2)(x - 2)] : (x / (x - 1))

Step 9: Invert the second fraction and multiply it by the first fraction.

Expression: (-2) / [(x + 2)(x - 2)] * ((x - 1) / x)

Step 10: Simplify the expression.

Expression: -2(x - 1) / (x(x + 2)(x - 2))

So, the simplified expression is -2(x - 1) / (x(x + 2)(x - 2)).