Question

5y+1/y²-9 - y+4/9-y² - 7-2y/9-y² =?

Answer 1

Ответ: 4/y-3

Объяснение:

5y+1/y²-9 - y+4/9-y² - 7-2y/9-y² =?

5y+1/y²-9 - y+4/-(y²-9) - 7-2y/-(y²-9)

5y+1/y²-9 + y+4/y²-9 + 7-2y/y²-9

5y+1+y+4+7-2y/y²-9

4y+12/(y-3)×(y+3)

4(y+3)/(y-3)×(y+3)

4/y-3 - Ответ

Answer 2

To simplify the expression, let's start by finding a common denominator for all the fractions involved. In this case, the denominator will be (9 - y²).

Now, let's simplify each fraction and combine them:

5y + 1/(y² - 9) - (y + 4)/(9 - y²) - (7 - 2y)/(9 - y²)

The first fraction: 1/(y² - 9) can be written as 1/((y + 3)(y - 3)) since y² - 9 is a difference of squares.

The second fraction: (y + 4)/(9 - y²) can be written as -(y + 4)/((y + 3)(y - 3)) since 9 - y² is the negation of y² - 9.

The third fraction: (7 - 2y)/(9 - y²) can be written as -(7 - 2y)/((y + 3)(y - 3)) since 9 - y² is the negation of y² - 9.

Now, we can rewrite the expression:

5y + 1/((y + 3)(y - 3)) - (y + 4)/((y + 3)(y - 3)) - (7 - 2y)/((y + 3)(y - 3))

Combining the fractions:

5y - (y + 4) - (7 - 2y)/((y + 3)(y - 3))

Now, let's simplify the expression further:

5y - y - 4 - (7 - 2y)/((y + 3)(y - 3))

Combining like terms:

4y - 4 - (7 - 2y)/((y + 3)(y - 3))

Next, let's simplify the expression (7 - 2y)/((y + 3)(y - 3)):

The numerator can be rewritten as -2(y - 3) since 7 - 2y = -2(y - 3).

Now, we have:

4y - 4 - 2(y - 3)/((y + 3)(y - 3))

Distribute the -2:

4y - 4 - 2y + 6)/((y + 3)(y - 3))

Simplify further:

2y + 2)/((y + 3)(y - 3))

Therefore, the simplified expression is (2y + 2)/((y + 3)(y - 3)).