X-15y/x²-25y²-5y/5xy-x²

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вопрос

To simplify the expression:

X - 15y / x² - 25y² - 5y / 5xy - x²

First, let's simplify the fractions separately:

X - 15y / x² - 25y² can be rewritten as (X - 15y) / (x - 5y)(x + 5y)

And

5y / 5xy - x² can be rewritten as y / xy - x² = y/x(y - x)

Now our expression becomes:

(X - 15y) / (x - 5y)(x + 5y) - y/x(y - x)

To find a common denominator, multiply the numerator and denominator of the first term by x:

(X - 15y) * x / x(x - 5y)(x + 5y) - y / x(y - x)

Now that we have a common denominator, we can combine the terms:

(Xx - 15xy) / x(x - 5y)(x + 5y) - y / x(y - x)

Expand the numerator:

Xx - 15xy - y / x(y - x)(x + 5y)

Now we need to find a common denominator for the remaining terms:

Xx - 15xy - y(x + 5y) / x(y - x)(x + 5y)

Expand the numerator:

Xx - 15xy - xy - 5y² / x(y - x)(x + 5y)

Combine like terms in the numerator:

Xx - 16xy - 5y² / x(y - x)(x + 5y)

Therefore, the simplified expression is:

(Xx - 16xy - 5y²) / x(y - x)(x + 5y)