SOLUTION: simplify this algebraic fraction: (y^2-y-6)/(y^2-25) ÷ (3-y)/(5-y) answer : (y+2)/(y+5) how is this simplified ?

Algebra ->  Expressions -> SOLUTION: simplify this algebraic fraction: (y^2-y-6)/(y^2-25) ÷ (3-y)/(5-y) answer : (y+2)/(y+5) how is this simplified ?      Log On


   

Question 1199800: simplify this algebraic fraction:
(y^2-y-6)/(y^2-25) ÷ (3-y)/(5-y)
answer : (y+2)/(y+5)
how is this simplified ?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You may be trying to show what is equivalent to this:
%28%28y%5E2-y-6%29%2F%28y%5E2-25%29%29%2F%28%283-y%29%2F%285-y%29%29


You can factor quadratic trinomials and difference of squares?
This works better on paper than through pure text, keyboard, and rendering tags.


---
Very obviously, about 1,
any real nonzero a, a%2Fa=1, or a and b real nonzero numbers, %28a%2Bb%29%2F%28a%2Bb%29=1.
for factor -1,
-1%28a-b%29=-1a-%28-1%29b=-a%2Bb.

Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!
simplify this algebraic fraction: (y^2-y-6)/(y^2-25) ÷ (3-y)/(5-y)
answer : (y+2)/(y+5)
how is this simplified ?

What did you try? I guess nothing!

%28%28y%5E2+-+y+-+6%29%2F%28y%5E2+-+25%29%29%2F%28%283+-+y%29%2F%285+-+y%29%29 ====> %28y%5E2+-+y+-+6%29%2F%28y%5E2+-+25%29 ÷ %283+-+y%29%2F%285+-+y%29

%28%28y+-+3%29%28y+%2B+2%29%29%2F%28%28y+-+5%29%28y+%2B+5%29%29 ÷ %283+-+y%29%2F%285+-+y%29 ----- Factoring 1st fraction's numerator and denominator

 ----- Applying KCF

 ---- Multiplying 2nd fraction's numerator and denominator by - 1 to
                                      match the factors in 1st fraction's numerator and denominator