Question

5((4)/(7))/1((5)/(21))-(5((2)/(15))*((3)/(22))+1((14)/(15)))​

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To simplify the given expression:

1. Let's simplify the numerator of the fraction on the left side: 5 * (4/7) = (20/7).

2. Now, let's simplify the denominator of the fraction on the left side: 1 * (5/21) = (5/21).

3. The left side of the expression becomes: (20/7) / (5/21).

4. To divide fractions, we invert the second fraction and multiply: (20/7) * (21/5) = (420/35).

5. Simplify the fraction (420/35) by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 35: 420/35 = 12/1 = 12.

Now let's simplify the right side of the expression:

1. Let's simplify the first term: 5 * (2/15) * (3/22) = (30/330) = (1/11).

2. Now, let's simplify the second term: 1 * (14/15) = (14/15).

3. The right side of the expression becomes: (1/11) + (14/15).

To add the fractions, we need a common denominator:

1. Find the least common multiple (LCM) of 11 and 15, which is 165.

2. Adjust the fractions to have the common denominator of 165: (1/11) * (15/15) = (15/165), (14/15) * (11/11) = (154/165).

3. The right side of the expression becomes: (15/165) + (154/165) = (169/165).

Finally, we can subtract the left side from the right side:

12 - (169/165).

Since the two terms have different denominators, we need a common denominator:

1. Find the least common multiple (LCM) of 165 and 1, which is 165.

2. Adjust the terms to have the common denominator of 165: 12 * (165/165) = (1980/165), (169/165) * (1/1) = (169/165).

3. The expression becomes: (1980/165) - (169/165) = (1811/165).

Therefore, the simplified form of the expression 5((4)/(7))/1((5)/(21))-(5((2)/(15))*((3)/(22))+1((14)/(15))) is (1811/165).