Question

((a+b)/ab):((a^2-b^2)/(2ab)

Answer 1

Ответ:

((a+b)/ab)

Объяснение:

Answer 2

To simplify the expression $\frac{{(a+b)/ab}}{{(a^2-b^2)/(2ab)}}$, you can follow these steps:

1. Simplify both the numerator and denominator separately:

Numerator: $\frac{{a+b}}{ab}$

Denominator: $\frac{{a^2-b^2}}{2ab}$

2. Now, simplify the fractions in the numerator and denominator:

Numerator: $\frac{a}{ab} + \frac{b}{ab} = \frac{1}{b} + \frac{1}{a}$

Denominator: $\frac{a^2-b^2}{2ab}$

3. Now, we can write the expression as:

$\frac{\frac{1}{b} + \frac{1}{a}}{\frac{a^2-b^2}{2ab}}$

4. To simplify further, we can factor the denominator $a^2 - b^2$ using the difference of squares:

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

5. Now, you can simplify by multiplying both the numerator and denominator by the reciprocal of the denominator:

$\frac{\frac{1}{b} + \frac{1}{a}}{\frac{(a+b)(a-b)}{2ab}} \cdot \frac{2ab}{(a+b)(a-b)}$

6. Cancel out common factors in the numerator and denominator:

$\frac{2a + 2b}{(a+b)(a-b)}$

7. Further simplify by factoring out a 2 from the numerator:

$\frac{2(a + b)}{(a+b)(a-b)}$

8. Finally, cancel out the common factor of $(a+b)$ in the numerator and denominator:

$\frac{2}{a-b}$

So, the simplified expression is $\frac{2}{a-b}$.