Question

X³+y³/x+y÷(x²-y²)+2y/x+y-xy/x²-y²​

Answer 1

Ответ:

Объяснение:

(x+y)(x^2-xy+y^2)/(x+y)*1/(x-y)(x+y) + 2y/(x+y)- xy/(x-y)(x+y)=((x^2-xy+y^2)+(2xy-2y^2)-xy)/(x^2-y^2)= (x^2-y^2)/(x^2-y^2)= 1

Answer 2

It seems like you've provided an expression with multiple terms and fractions. To simplify this expression, let's break it down step by step:

Expression:

(x³ + y³) / (x + y) ÷ (x² - y²) + 2y / (x + y) - xy / (x² - y²)

Step 1: Factor the numerator of the first fraction (x³ + y³):

(x³ + y³) = (x + y)(x² - xy + y²)

Now, our expression looks like this:

((x + y)(x² - xy + y²)) / (x + y) ÷ (x² - y²) + 2y / (x + y) - xy / (x² - y²)

Step 2: Cancel out the common factors in each fraction:

The (x + y) terms in the first and third fractions can be canceled out:

(x² - xy + y²) / (x² - y²) + 2y / (x + y) - xy / (x² - y²)

Step 3: Factor the denominator of the first fraction (x² - y²):

(x² - y²) = (x + y)(x - y)

Now, our expression looks like this:

(x² - xy + y²) / ((x + y)(x - y)) + 2y / (x + y) - xy / ((x + y)(x - y))

Step 4: Find a common denominator for all three fractions, which is (x + y)(x - y):

[(x² - xy + y²) + 2y(x - y) - xy] / ((x + y)(x - y))

Step 5: Simplify the numerator by expanding and combining like terms:

(x² - xy + y² + 2xy - 2y² - xy) / ((x + y)(x - y))

Now, simplify further by combining like terms:

(x² + y²) / ((x + y)(x - y))

So, the simplified expression is:

(x² + y²) / ((x + y)(x - y))

This is the simplified form of the given expression.