Simplifying Rational Expressions?

Question

3z^2+z over 18+6


5x-25 over x^2-25


3x^2-3 over 6x-6


y^2+2y-3 over y^2 -3y+2

m-3 over 3-m

Answer 1

(3z^2+z) / (18+6) =
z(3z+1)/24

(5x-25) / (x^2-25) =
5(x-5) / (x+5)(x-5) =
5 / (x+5)

(3x^2-3) / (6x-6) =
3(x^2 -1) / 6(x-1) =
(x+1)(x-1) / 2(x-1) =
(x+1)/2

(y^2+2y-3) / (y^2 -3y+2) =
(y+3)(y-1) / (y-2)(y-1) =
(y+3) / (y-2)

(m-3) / (3-m) =
(m-3) / -(m-3) =
1 / -1 =
-1

Answer 2

1. Note: I think you mean 18z+6 so i'll solve it for that scenario
(3z^2+z)/(18z+6) = z(3z+1)/6(3z+1)=z/6

2. (5x-25)/(x^2-25) = 5(x-5)/(x+5)(x-5) = 5/(x+5)

3. (3x^2-3)/(6x-6) = 3(x^2-1)/6(x-1) = (x+1)(x-1)/2(x-1) =(x+1)/2

4. (y^2+2y-3)/(y^2-3y+2) = (y+1)(y-3)/(y+1)(y+2) = (y-3)/(y+2)

5. (m-3)/(3-m) = -(3-m)/(3-m) = -1