Question

(a+7b/a^2-7ab - a-7b/a^2+7ab) : 28b^2/49b^2-a^2=

Answer 1

Ответ:

(0+0+0)/28*b^2/49*b^2-a^2

0/28*b^2/49*b^2-a^2

0-a^2

-a^2

Пошаговое объяснение:

Answer 2

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

Expression:

$$\frac{\left(\frac{a + 7b}{a^2 - 7ab} - \frac{a - 7b}{a^2 + 7ab}\right)}{\frac{28b^2}{49b^2 - a^2}}$$

Step 1: Combine the fractions in the numerator:

$$\frac{\frac{(a + 7b)(a^2 + 7ab) - (a - 7b)(a^2 - 7ab)}{(a^2 - 7ab)(a^2 + 7ab)}}{\frac{28b^2}{49b^2 - a^2}}$$

Step 2: Expand and simplify the numerators of the fractions in the numerator:

$$\frac{\frac{a^3 + 7a^2b + 7a^2b + 49ab^2 - (a^3 - 7a^2b - 7a^2b + 49ab^2)}{(a^2 - 7ab)(a^2 + 7ab)}}{\frac{28b^2}{49b^2 - a^2}}$$

$$\frac{\frac{a^3 + 7a^2b + 7a^2b + 49ab^2 - a^3 + 7a^2b + 7a^2b - 49ab^2}{(a^2 - 7ab)(a^2 + 7ab)}}{\frac{28b^2}{49b^2 - a^2}}$$

$$\frac{\frac{98ab^2}{(a^2 - 7ab)(a^2 + 7ab)}}{\frac{28b^2}{49b^2 - a^2}}$$

Step 3: Invert and multiply by the reciprocal of the second fraction:

$$\frac{98ab^2}{(a^2 - 7ab)(a^2 + 7ab)} \cdot \frac{49b^2 - a^2}{28b^2}$$

Step 4: Cancel out common factors and simplify:

$$\frac{98ab^2(49b^2 - a^2)}{28b^2(a^2 - 7ab)(a^2 + 7ab)}$$

Step 5: Further simplify by canceling out common factors if possible, and rewriting the expression:

$$\frac{7(49b^2 - a^2)}{2(a^2 - 7ab)(a^2 + 7ab)}$$

So, the simplified expression is:

$$\frac{7(49b^2 - a^2)}{2(a^2 - 7ab)(a^2 + 7ab)}$$