Question

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

Answer 1

$\displaystyle \tt{} \ \ \ \frac{(a+b)^{2}}{ab}-\frac{(a-b)^{2}}{ab}=\frac{(a+b)^{2}-(a-b)^{2}}{ab}=\\\\\\=\frac{a^{2}+2ab+b^{2}-(a^{2}-2ab+b^{2})}{ab}=\frac{4ab}{ab}=4;$

Answer 2

Ответ:4

Объяснение:

(a+b)^2/ab -(a-b) ^2/ab=((a+b)^2-(a-b) ^2)/2=(a^2+2ab+b^2-a^2+2ab-b^2)ab=4ab/ab=4

Ответ:(a+b)^2/ab - (a-b)^2/ab=4

Answer 3

First, let's simplify each term individually:

1. (a+b)^2/ab

Expanding the square, we get:

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(a+b)^2 = a^2 + 2ab + b^2

So, (a+b)^2/ab becomes:

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(a^2 + 2ab + b^2) / ab
= a/ab + 2b/ab + b^2/ab
= 1/a + 2/b + (b/a)^2

2. (a-b)^2/ab

Expanding the square, we get:

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(a-b)^2 = a^2 - 2ab + b^2

So, (a-b)^2/ab becomes:

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

Now, we can subtract the second term from the first term:

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(1/a + 2/b + (b/a)^2) - (1/a - 2/b + (b/a)^2)
= 1/a + 2/b + (b/a)^2 - 1/a + 2/b - (b/a)^2
= 4/b

Therefore, (a+b)^2/ab - (a-b)^2/ab = 4/b.