5x-4 /2 + 4x+4/9

a) To simplify the expression, we need to find a common denominator for the fractions. The common denominator for 2 and 9 is 18.

So, we have:

(5x - 4)/2 + (4x + 4)/9

To get the fractions to have a common denominator of 18, we need to multiply the first fraction by 9/9 and the second fraction by 2/2:

(9(5x - 4))/18 + (2(4x + 4))/18

Simplifying further:

(45x - 36)/18 + (8x + 8)/18

Now, we can combine the fractions:

(45x - 36 + 8x + 8)/18

Combining like terms:

(53x - 28)/18

So, the simplified expression is (53x - 28)/18.

b) To simplify the expression, we need to find a common denominator for the fractions. The common denominator for 2x^2y + 6 and 2x^2y is 2x^2y(2x^2y + 6).

So, we have:

(x^2y - 6)/(2x^2y + 6) - (xy^2)/(2x^2y)

To get the fractions to have a common denominator of 2x^2y(2x^2y + 6), we need to multiply the first fraction by (2x^2y)/(2x^2y) and the second fraction by (2x^2y + 6)/(2x^2y + 6):

((x^2y - 6)(2x^2y))/((2x^2y + 6)(2x^2y)) - ((xy^2)(2x^2y + 6))/((2x^2y)(2x^2y + 6))

Simplifying further:

(2x^4y^2 - 12x^2y)/((2x^4y^2 + 6x^2y)(2x^2y)) - (2x^3y^3 + 6xy^2)/((2x^4y^2 + 6x^2y)(2x^2y))

Now, we can combine the fractions:

(2x^4y^2 - 12x^2y - 2x^3y^3 - 6xy^2)/((2x^4y^2 + 6x^2y)(2x^2y))

So, the simplified expression is (2x^4y^2 - 12x^2y - 2x^3y^3 - 6xy^2)/((2x^4y^2 + 6x^2y)(2x^2y)).

c) To simplify the expression, we need to find a common denominator for the fractions. The common denominator for 3xy^2 and 3xy^2 is 3xy^2.

So, we have:

(4x - 1)/(3xy^2) - (7x - 1)/(3xy^2)

Since the fractions already have a common denominator, we can combine them directly:

(4x - 1 - 7x + 1)/(3xy^2)

Combining like terms:

(-3x)/(3xy^2)

Simplifying further:

-1/y^2

So, the simplified expression is -1/y^2.