Question

Need help of simplifying each sum or difference

Answer 1

First you need to get a common denominator. The first two problems already have a common denominator, so you just have to find the sum and difference of the two problems, respectively. 

6.) (9y-3)/(y^2-5)

8.) 3/xy^3

Two find a common denominator, find the smallest value that has BOTH denominators as factors. 

10.) 8x^3*y^3 is the common denominator

Answer: 2/(8*x^3*y^3)

12.) Factor x^2 + 4x + 4 to get (x+2)(x+2)

Therefore, x+2 is already part of x^2 + 4x + 4

(x+4)/(x^2+4x+4)

14.) Factor both denominators..

4(y+2) and y(y+2)

So the common denominator would be 4y(y+2)

The first fraction is missing a "y" so multiply the numerator by y to get y^2

The second fraction is missing a "4" so multiply the numerator by 4 to get 4

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

So can factor the numerator to get (y+2)(y-2). There if a (y+2) on top and bottom so they cancel out. 

Answer: (y-2)/4y