Question

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

Answer 1

приводим к общеу заменателю и получаем ответ: (2+ab)/(a(2+b))

Answer 2

ответ: (2+ab)/(a(2+b))

Answer 3

To simplify the given expression, let's start by focusing on each fraction separately:

Fraction 1: (2 - ab) / (2a + ab)

Fraction 2: (2b) / (2 + b)

Now, let's simplify each fraction step by step:

Fraction 1: We can notice that the numerator (2 - ab) can be factored out a negative sign, giving us -(ab - 2). So, the fraction becomes:

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

Fraction 2: Since the denominator has a common factor of 2, we can simplify it by factoring out 2:

2b / (2 + b) = 2b / (1 * 2 + b) = 2b / (1 * (2 + b)) = 2b / (2(1 + b))

Now, let's combine the two fractions:

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

To add the fractions, we need a common denominator. The common denominator in this case is (2a + ab) * 2(1 + b).

Now, let's find the equivalent fractions with the common denominator:

Fraction 1: Multiply the numerator and denominator by 2(1 + b):

-(ab - 2) * 2(1 + b) / [(2a + ab) * 2(1 + b)]

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

= -2(ab - 2)(1 + b) / [2(1 + b)(2a + ab)]

= -2(ab - 2)(1 + b) / [4a(1 + b) + 2ab(1 + b)]

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

= -2(ab - 2)(1 + b) / [4a + 6ab + 2ab^2]

Fraction 2: Multiply the numerator and denominator by (2a + ab):

2b * (2a + ab) / [(2a + ab) * 2(1 + b)]

= 2b(2a + ab) / [2(1 + b)(2a + ab)]

= 2b(2a + ab) / [4a(1 + b) + 2ab(1 + b)]

= 2b(2a + ab) / [4a + 4ab + 2ab + 2ab^2]

= 2b(2a + ab) / [4a + 6ab + 2ab^2]

Now, we can rewrite the expression as:

[-2(ab - 2)(1 + b) + 2b(2a + ab)] / [4a + 6ab + 2ab^2]

Simplifying the numerator:

[-2(ab - 2)(1 + b) + 2b(2a + ab)]

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

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

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

= -4b + 2ab - 4 + 4ab + 2b^2

= 6ab - 4b + 2b^2 -