SOLUTION: Let (ax+b)/(x^2-1)=a/(x+1)+b/(x-1). Find a and b. This is from the Pre-Cal Conics, rotation of axes section. Any help would be awesome. thank you

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Let (ax+b)/(x^2-1)=a/(x+1)+b/(x-1). Find a and b. This is from the Pre-Cal Conics, rotation of axes section. Any help would be awesome. thank you       Log On


   

Question 869890: Let (ax+b)/(x^2-1)=a/(x+1)+b/(x-1). Find a and b.
This is from the Pre-Cal Conics, rotation of axes section. Any help would be awesome. thank you
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
?
The right hand side,

%28a%28x-1%29%2Bb%28x%2B1%29%29%2F%28%28x%2B1%29%28x-1%29%29
%28ax-a%2Bbx%2Bb%29%2F%28x%5E2-1%29

Now, the numerators of left and right are the same. We started with the equality, so now just adjust numerators to same form and compare corresponding terms.

ax%2Bb=ax-a%2Bbx%2Bb
ax%2Bb=ax%2Bbx%2Bb-a
ax%2Bb=%28a%2Bb%29x%2B%28b-a%29

The way those correspond,
a=a%2Bb and b=b-a
?
a=a%2B%28b-a%29
0=b-a
b=a
-
b=b-(a+b)
b=-a
One possibility is, a=0 and b=0.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Let (ax+b)/(x^2-1)=a/(x+1)+b/(x-1). Find a and b.
This is from the Pre-Cal Conics, rotation of axes section. Any help would be awesome. thank you 


%28ax+%2B+b%29%2F%28x%5E2+-+1%29+=+a%2F%28x+%2B+1%29+%2B+b%2F%28x+-+1%29

ax + b = a(x - 1) + b(x + 1) ------ Multiplying by LCD, x%5E2+-+1, or (x - 1)(x + 1)

ax + b = ax - a + bx + b

ax - ax + a = bx + b - b

highlight_green%28a+=+bx%29, and highlight_green%28a%2Fx+=+b%29