Question

(а+7/а-7 - а-7/а+7):14а/49-а^2

Answer 1

В конце, если что, ответ получается -2

Answer 2

To simplify the expression, let's perform the operations step by step:

1. Simplify the fraction inside the parenthesis: (а + 7/а - 7 - а - 7/а + 7)

2. Find the common denominator for the fractions inside the parenthesis. The common denominator is (а)(а + 7)(а - 7): [(а)(а + 7)(а - 7) + 7(а - 7) - (а)(а + 7) - 7(а)] / [(а)(а + 7)(а - 7)]

3. Expand the terms inside the parenthesis: [а^3 + 7а^2 - 7а^2 - 49а + 7а - 49 - а^2 - 7а] / [(а)(а + 7)(а - 7)]

4. Combine like terms: [а^3 + 7а - 49 - а^2 - 7а] / [(а)(а + 7)(а - 7)]

5. Simplify further: (а^3 - а^2 + 7а - 49) / [(а)(а + 7)(а - 7)]

Now, let's simplify the denominator: 14а/49 - а^2

The common denominator for the terms is 49, so we can rewrite the expression as: (14а - 49а^2) / 49

Now, to simplify the entire expression, we divide the fraction inside the parenthesis by the denominator: [(а^3 - а^2 + 7а - 49) / (а)(а + 7)(а - 7)] ÷ [(14а - 49а^2) / 49]

To divide fractions, we multiply by the reciprocal of the second fraction: [(а^3 - а^2 + 7а - 49) / (а)(а + 7)(а - 7)] * [49 / (14а - 49а^2)]

Now, we factor out common terms: [а^3 - а^2 + 7а - 49] / [а(а + 7)(а - 7)] * [49 / (7а(2 - а))]

Now, we can cancel out common factors: [(а^3 - а^2 + 7а - 49) / (а(а + 7)(а - 7))] * [1 / (2 - а)]

Finally, we have: (а^3 - а^2 + 7а - 49) / [а(а + 7)(а - 7)(2 - а)]

This is the simplified form of the expression.