SOLUTION: I need help with this question it's quite hard and I don't get it. I sincerely request a step-by-step answer. Simplify: b^2-a^2/ 2a^2+ab-3b^2 Thank you so much.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help with this question it's quite hard and I don't get it. I sincerely request a step-by-step answer. Simplify: b^2-a^2/ 2a^2+ab-3b^2 Thank you so much.      Log On


   

Question 1185373: I need help with this question it's quite hard and I don't get it. I sincerely request a step-by-step answer.
Simplify:
b^2-a^2/ 2a^2+ab-3b^2
Thank you so much.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
I need help with this question it's quite hard and I don't get it. I sincerely request a step-by-step answer.
Simplify:
b^2-a^2/ 2a^2+ab-3b^2
Thank you so much.
~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

The numerator of the given fraction has factoring


    b^2 - a^2 = (b+a)*(b-a).      It is classic factoring; everybody knows it (or must know it).


The denominator of the given fraction has factoring


    2a^2 + ab - 3b^2 = (a-b)*(2a+3b).     You can check directly that it is true.


When you form the fraction, the factors (b-a) cancel each other.


The rest is


    %28b%5E2-a%5E2%29%2F%282a%5E2%2Bab-3b%5E2%29 = - %28b%2Ba%29%2F%282a%2B3b%29.        ANSWER

Solved and completed.



Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Given expression is
b^2-a^2/ 2a^2+ab-3b^2


Maybe not what was really given to you.
Have this instead?
(b^2-a^2)/ (2a^2+ab-3b^2)

The (almost) obvious factorizations give the expression
%28%28b-a%29%28b%2Ba%29%29%2F%28%282a%2B3b%29%28a-b%29%29
and you can continue from here.