Х²/у+6-у²/у+6

To simplify the expression (х²/у + 6 - у²/у + 6), we first need to find a common denominator for the fractions. In this case, the common denominator is (у + 6).

So, let's convert each fraction to have the common denominator (у + 6):

х²/у + 6 - у²/у + 6

To convert the first fraction, we multiply the numerator and denominator by (у + 6):

х²(у + 6)/(у(у + 6)) + 6

For the second fraction, we don't need to do anything since it already has the common denominator:

• у²/у + 6

Now, let's simplify:

х²(у + 6)/(у(у + 6)) - у²/у + 6

To combine the fractions, we need to get rid of the denominators. We can do this by multiplying each fraction by the necessary factors:

(х²(у + 6) - у²(у + 6))/(у(у + 6)) + 6(у(у + 6))/(у(у + 6))

Simplifying further:

(х²у + 6х² - у³ - 6у²)/(у(у + 6)) + 6у(у + 6)/(у(у + 6))

Now, let's combine like terms:

(х²у + 6х² - у³ - 6у² + 6у(у + 6))/(у(у + 6))

Simplifying:

(х²у + 6х² - у³ - 6у² + 6у² + 36у)/(у(у + 6))

Combining like terms again:

(х²у + 6х² - у³ + 36у)/(у(у + 6))

So, the simplified expression is (х²у + 6х² - у³ + 36у)/(у(у + 6)).