SOLUTION: Simplify the following algebraic fraction : (a^2-3a-4)/(a^2-4) x (2-a-a^2) /(a^2-1) answer: (4-a)/(a-2) how is this worked out ?

Algebra ->  Expressions -> SOLUTION: Simplify the following algebraic fraction : (a^2-3a-4)/(a^2-4) x (2-a-a^2) /(a^2-1) answer: (4-a)/(a-2) how is this worked out ?      Log On


   

Question 1199801: Simplify the following algebraic fraction :
(a^2-3a-4)/(a^2-4) x (2-a-a^2) /(a^2-1)
answer: (4-a)/(a-2)
how is this worked out ?
Found 3 solutions by josgarithmetic, MathLover1, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
(a^2-3a-4)/(a^2-4) x (2-a-a^2) /(a^2-1)

%28%28a%5E2-3a-4%29%2F%28a%5E2-4%29%29%28%282-a-a%5E2%29+%2F%28a%5E2-1%29%29
You need to know how to factorize degree-two trinomials and difference of squares. (and understand convenience of -1 as a factor).

%28%28a%5E2-3a-4%29%28-1%29%28a%5E2%2Ba-2%29%29%2F%28%28a%5E2-4%29%28a%5E2-1%29%29



Look for and cancel factors of 1, numerator and denominator same factor


%28%28-1%29%28a-4%29%28a-1%29%29%2F%28%28a%2B2%29%28a-1%29%29

%28%28-1%29%28a-4%29cross%28%28a-1%29%29%29%2F%28%28a%2B2%29cross%28%28a-1%29%29%29

and then,.....!
PROBLEM: There appears to be one or two mistakes there. Pure text is very difficult to work with. This kind of arithmetic works better on paper with pencil.

Answer by MathLover1(20850) About Me  (Show Source):
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify the following algebraic fraction :
(a^2-3a-4)/(a^2-4) x  (2-a-a^2) /(a^2-1)
answer: (4-a)/(a-2)
how is this worked out ?

What have you tried? Nothing I guess!

%28%28a%5E2+-+3a+-+4%29%2F%28a%5E2+-+4%29%29+%2A+%28%282+-+a+-+a%5E2%29%2F%28a%5E2+-+1%29%29

 ------ Factoring ALL numerators and denominators

 ------ Multiplying 2nd fraction's numerator by - 1 to
                                            match factor in denominator