Question

(16b/a-16a/b)*1/4a+4bупростить/-дробь

Answer 1

(16в/а-16а/в)*1/(4а+4в)=

16(в²-а²)/((ав*(а+в)*4)=4(в-а)/ав

Answer 2

To simplify the expression (16b/a - 16a/b) * (1/4a + 4b), we'll follow these steps:

Step 1: Find the common denominator for the fractions. Step 2: Perform the operations within the parentheses. Step 3: Simplify the result.

Let's begin:

Step 1: Find the common denominator for the fractions. The common denominator for a and b is ab. So, we need to rewrite the expression with the common denominator.

(16b/a - 16a/b) * (1/4a + 4b) = [(16b * b) / (a * b) - (16a * a) / (a * b)] * [(1 * b) / (4a * b) + (4b * a) / (4a * b)]

Step 2: Perform the operations within the parentheses.

(16b * b) / (a * b) = 16b^2 / ab (16a * a) / (a * b) = 16a^2 / ab (1 * b) / (4a * b) = b / (4a * b) = 1 / 4a (4b * a) / (4a * b) = 4ab / (4a * b) = 1 / a

Step 3: Simplify the result.

Now, the expression becomes:

(16b^2 / ab - 16a^2 / ab) * (1 / 4a + 1 / a)

To add the two fractions inside the parentheses, we need a common denominator, which is 4a.

1 / 4a + 1 / a = (1 + 4) / 4a = 5 / 4a

So, the expression becomes:

(16b^2 / ab - 16a^2 / ab) * (5 / 4a)

Now, to simplify further, we can factor out a common term in the numerator:

(16b^2 - 16a^2) / ab * (5 / 4a)

Next, we can simplify the term in the numerator:

16(b^2 - a^2) = 16(b + a)(b - a)

Now, the expression becomes:

(16(b + a)(b - a)) / ab * (5 / 4a)

We can cancel out common factors in the numerator and denominator:

(4(b + a)(b - a)) / b * (5 / 4)

Finally, we can simplify further:

(5(b + a)(b - a)) / b

So, the simplified expression is (5(b + a)(b - a)) / b.