Question

what is the simplified form of... (5/3y-2)-(4/9y^2-4)

Answer 1

the binomial can be factored using the difference of squares formula, because both terms are perfect squares

The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b)

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

Multiply -1 by the (4)/((3y-2)(3y+2)) inside the parentheses.

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

Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of (3y+2)(3y-2). The (5)/((3y-2)) expression needs to be multiplied by ((3y+2))/((3y+2)) to make the denominator (3y+2)(3y-2).
(5)/(3y-2)*(3y+2)/(3y+2)-(4)/((3y-2)(3y+2))

Multiply the expression by a factor of 1 to create the least common denominatorof (3y+2)(3y-2).

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

The numerators of expressions that have equal denominators can be combined.

In this case, ((5(3y+2)))/((3y+2)(3y-2)) and -(4)/((3y-2)(3y+2)) have the same denominator of (3y+2)(3y-2), so the numerators can be combined.

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

Simplify the numerator of the expression.
(15y+10-4)/((3y+2)(3y-2))

Subtract 4 from 10 to get 6.
(15y+6)/((3y+2)(3y-2))

Factor out the GCF of 3 from each term in the polynomial.
(3(5y)+3(2))/((3y+2)(3y-2))

Factor out the GCF of 3 from 15y+6.
(3(5y+2))/((3y+2)(3y-2))

Answer 2

15y+6/(3y+2)(3y+2)?

Answer 3

or is it (3y-2)(3y+2) on the bottom?