\frac{1}{a-b} - \frac{1}{b-a} - \frac{2a}{a^2-b^2}

Предыдущий
вопрос Следующий
вопрос

To simplify the given expression, we can first write it in terms of a single fraction.

Using the identity (\frac{1}{a-b} = -\frac{1}{b-a}), we can combine the first two terms:

(\frac{1}{a-b} - \frac{1}{b-a} = \frac{1}{a-b} + \frac{1}{a-b} = \frac{2}{a-b})

Next, we can simplify the third term using the difference of squares formula:

(\frac{2a}{a^2-b^2} = \frac{2a}{(a+b)(a-b)} = \frac{2a}{a-b})

Combining all the terms together, we get:

(\frac{1}{a-b} - \frac{1}{b-a} - \frac{2a}{a^2-b^2} = \frac{2}{a-b} - \frac{2a}{a-b} = \frac{2-2a}{a-b})

Therefore, the simplified form of the given expression is (\frac{2-2a}{a-b}).