Question

1) (x+5y/x^-5xy - x-5y/x^+5xy)* 25y^-x^/5y^ 2) (a-2b/a^+2ab - a+2ab/a^-2ab): 4b^/4b^-a ДЕТАЛЬНО УПРОСТИТЕ ПОЖАЛУЙСТА

Answer 1

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Answer 2

To simplify the given expressions, we need to follow the order of operations (PEMDAS) and combine like terms where possible. Let's simplify each expression step-by-step:

1. (x+5y/x^-5xy - x-5y/x^+5xy) * 25y^-x^/5y^

Step 1: Simplify the expressions inside the parentheses. (x + 5y) / (x^-5xy) - (x - 5y) / (x^+5xy)

Step 2: Deal with the exponents. (x + 5y) / (1/x^5y) - (x - 5y) / (1/x^5y)

Step 3: Flip the denominators (change the sign of the exponent). (x + 5y) * x^5y - (x - 5y) * x^5y

Step 4: Expand and combine like terms. x^6y + 5x^5y^2 - x^6y + 5x^5y^2

Step 5: Simplify further. 2x^5y^2

Now let's simplify the second part of the expression:

25y^-x^/5y^

Step 1: Deal with the negative exponent. 25 * (1/y^x) / 5y^1

Step 2: Simplify. 5 * (1/y^x)

The final expression is:

2x^5y^2 * (5 / y^x)

2. (a-2b/a^+2ab - a+2ab/a^-2ab) : 4b^/4b^-a

Step 1: Simplify the expressions inside the parentheses. (a - 2b) / (a^ + 2ab) - (a + 2ab) / (a^ - 2ab)

Step 2: Deal with the exponents. (a - 2b) / (1/a^2ab) - (a + 2ab) / (1/a^-2ab)

Step 3: Flip the denominators (change the sign of the exponent). (a - 2b) * a^2ab - (a + 2ab) * a^-2ab

Step 4: Expand and combine like terms. a^3b - 2a^2b^2 - a^-1b + 2b^2

Step 5: Simplify further. a^3b - 2a^2b^2 - b^-1(1/a) + 2b^2

Step 6: More simplification. a^3b - 2a^2b^2 - b^(-1+1/a) + 2b^2

Now let's simplify the second part of the expression:

4b^/4b^-a

Step 1: Deal with the negative exponent. 4 * (1/b^a) / 4b^1

Step 2: Simplify. (1/b^a) / b

The final expression is:

(a^3b - 2a^2b^2 - b^(-1+1/a) + 2b^2) / (1/b^a) / b

To simplify further, remember that dividing by a fraction is equivalent to multiplying by its reciprocal:

(a^3b - 2a^2b^2 - b^(-1+1/a) + 2b^2) * (b^a)