Question

(a/b-b/a)*3ab/a+b Выполните действия

Answer 1

$(\frac{a}{b} -\frac{b}{a} )*\frac{3ab}{a+b} =\frac{a^{2}-b^{2} }{ab} *\frac{3ab}{a+b} =\frac{(a-b)(a+b)}{ab}*\frac{3ab}{a+b} =3(a-b)$

Answer 2

To simplify the expression (a/b-b/a)*3ab/a+b, we can start by finding the common denominator for the terms in the denominator of the fraction:

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

Using the difference of squares formula, we can simplify the numerator:

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

Substituting this back into the original expression, we get:

(a/b-b/a)*3ab/a+b = ((a+b)(a-b))/(ab) * 3ab/(a+b)

We can cancel out the (a+b) term in the numerator and denominator to simplify further:

((a+b)(a-b))/(ab) * 3ab/(a+b) = (a-b) * 3b = 3b(a-b)

Therefore, the simplified expression is 3b(a-b).