Question

(a/a+b-a³/a²+2ab+b²):(a/a+b-a²/a²-b²)​

Answer 1

Ответ:

1) a/a+b-a³/a²+2ab+b²= a^2+b-a^3+2a^2b+a^2b^2/a^2

2)a/a+b-a²/a²-b²=a^2+b-a^2-a^2b/a^2

3) a^2+b-a^3+2a^2b+a^2b^2*a^2/a^2*a^2+b-a^2-a^2b=a+2a^2b=a(1+2ab)

Answer 2

To simplify the given expression:

cssCopy code
(a/a+b-a³/a²+2ab+b²) : (a/a+b-a²/a²-b²)

Let's begin by finding the LCM of the denominators:

cssCopy code
LCM(a² + 2ab + b², a² - b²) = (a + b)(a - b)(a² + 2ab + b²)

Next, we can rewrite each term in the expression using this LCM:

cssCopy code
a/a+b-a³/a²+2ab+b² = (a(a - b)(a + b))/(a + b)(a - b)(a² + 2ab + b²)
a/a+b-a²/a²-b² = (a(a + b)(a - b))/(a + b)(a - b)(a² + 2ab + b²)

Now we can simplify the expression by canceling out common factors:

lessCopy code
(a/a+b-a³/a²+2ab+b²) : (a/a+b-a²/a²-b²)
= [(a(a - b)(a + b))/(a + b)(a - b)(a² + 2ab + b²)] : [(a(a + b)(a - b))/(a + b)(a - b)(a² + 2ab + b²)]
= [(a - b)/(a² + 2ab + b²)] : [(a + b)/(a² - b²)]
= (a - b)(a² - b²)/(a + b)(a² + 2ab + b²)
= [(a - b)(a + b)(a - b)]/[(a + b)(a + b)(a - b)]
= (a - b)/(a + b)   [canceling out the common factor (a - b)/(a - b)]

Therefore, the simplified expression is (a - b)/(a + b).