Question

А/а+7-(а-7)^2•(1/а^2-49+1/а^2-49+1/а^2-14а+49)

Answer 1

Ответ:    $\frac{7-2a}{a+7}$ .

Объяснение:

$\frac{a}{a+7}-(a-7)^2\cdot \Big (\frac{1}{a^2-49}+\frac{1}{a^2-49}+\frac{1}{a^2-14a+49}\Big )=\\\\=\frac{a}{a+7}-(a-7)^2\cdot \Big (\frac{2}{(a-7)(a+7)}+\frac{1}{(a-7)^2}\Big )=\\\\=\frac{a}{a+7}-(a-7)^2\cdot \frac{2(a-7)+(a+7)}{(a-7)^2(a+7)}=\\\\=\frac{a}{a+7}-\frac{2a-14+a+7}{a+7}=\frac{a}{a+7}-\frac{3a-7}{a+7}=\frac{a-3a+7}{a+7}=\frac{7-2a}{a+7}$

Answer 2

Let's simplify the expression step by step:

1. Combine like terms inside the parentheses:

scssCopy code
(а-7)^2 = (а-7) * (а-7) = а^2 - 14а + 49

2. Replace the expression with the simplified form:

scssCopy code
а+7 - (а^2 - 14а + 49) • (1/а^2 - 49 + 1/а^2 - 49 + 1/а^2 - 14а + 49)

3. Now, let's combine like terms inside the second set of parentheses:

Copy code
1/а^2 - 49 + 1/а^2 - 49 + 1/а^2 - 14а + 49

4. Simplify each term:

Copy code
1/а^2 - 98 + 1/а^2 - 14а + 49

5. Combine like terms again:

Copy code
2/а^2 - 14а - 49

Now the expression becomes:

scssCopy code
а + 7 - (а^2 - 14а + 49) • (2/а^2 - 14а - 49)

6. Distribute the expression inside the parentheses:

scssCopy code
а + 7 - 2(а^2 - 14а + 49)/а^2 - 14а - 49

7. Further simplify the expression inside the parentheses:

scssCopy code
а + 7 - 2(а^2 - 14а + 49)/а^2 - 63

8. To continue simplification, let's find a common denominator for the fraction:

scssCopy code
а^2 - 63 = (а - 9)(а + 7)

9. Now, let's rewrite the expression with the common denominator:

scssCopy code
а + 7 - 2(а^2 - 14а + 49)/(а - 9)(а + 7)

10. Simplify further by canceling out the common factors:

Copy code
а + 7 - 2/а - 9

11. Combine like terms:

Copy code
а + 7 - 2/а - 9 = а - 2/а - 2

So, the simplified expression is а - 2/а - 2.