Question

ПОМОГИТЕ!выполните действия А) (b/c-c/b)*bc/b-c Б)3a-18/a^2-25 * (1- 1/6-a) В) (a/a+1 +1):2а/а+1

Answer 1

А: 1) b/c-c/b=b^2-c^2/bc=(b-c)(b+c)/bc
2) (b-c)(b+c)/bc*bc/b-c=b+c
В: 1) (a/a+1) +1):2а/а+1=(2a+1/a+1)*(a+1)/2a)=(2a+1)/2a
Б: непонятно: ты умножаешь 1-1/6-а на всю дробь, или только на знаменатель?

Answer 2

А) (b/c-c/b)*bc/(b-c)

Let's simplify the expression step by step:

1. Find the common denominator for (b/c) and (c/b) which is bc:

(b/c-c/b) = (b^2 - c^2)/bc

2. Now we can substitute this back into the original expression:

(b/c-c/b)*bc/(b-c) = [(b^2 - c^2)/bc]*bc/(b-c)

3. Simplify by canceling out the common factor (b-c) in the denominator with the denominator in the first fraction:

[(b^2 - c^2)/bc]*bc/(b-c) = (b+c)

So the final answer is (b+c).

Б) 3a-18/a^2-25 * (1- 1/(6-a))

Let's simplify the expression step by step:

1. Factor the denominator a^2-25 as (a+5)(a-5):

3a-18/[(a+5)(a-5)] * (1- 1/(6-a))

2. Find the common denominator for 1 and (6-a) which is (6-a):

3a-18/[(a+5)(a-5)] * [(6-a)/(6-a) - 1/(6-a)]

3. Simplify by combining the fractions in the parentheses:

3a-18/[(a+5)(a-5)] * [(6-a-1)/((6-a)*(6-a))]

4. Simplify by canceling out the common factor (6-a) in the numerator and denominator:

3a-18/[(a+5)(a-5)] * [-1/((6-a))]

5. Simplify by canceling out the factor of -3 in the numerator and -1 in the denominator:

(a-6)/(5(a+5))

So the final answer is (a-6)/(5(a+5)).

В) (a/a+1 +1):2а/а+1

Let's simplify the expression step by step:

1. Combine the terms in the numerator using a common denominator (a+1):

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

2. Substitute this back into the original expression:

(2a+1)/(a+1) : 2a/(a+1)

3. Invert the second fraction and multiply:

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

So the final answer is (2a+1)/2a.