SOLUTION: {{{1/(x(x+1))=a/x-b/(x+1)}}} In the euation above, a and b are constants. If the equation is true for all positive values of x, what is the value of b? A) -1 B) 1 C) 2 D) 4

Algebra ->  Expressions -> SOLUTION: {{{1/(x(x+1))=a/x-b/(x+1)}}} In the euation above, a and b are constants. If the equation is true for all positive values of x, what is the value of b? A) -1 B) 1 C) 2 D) 4      Log On


   

Question 1043309: 1%2F%28x%28x%2B1%29%29=a%2Fx-b%2F%28x%2B1%29
In the euation above, a and b are constants. If the equation is true for all positive values of x, what is the value of b?
A) -1
B) 1
C) 2
D) 4
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%28x%28x%2B1%29%29=a%2Fx-b%2F%28x%2B1%29

%281%2F%28x%28x%2B1%29%29%29%28x%28x%2B1%29%29=%28a%2Fx-b%2F%28x%2B1%29%29%28x%28x%2B1%29%29

1=a%28x%2B1%29-bx

1=ax%2Ba-bx

Arrange into expressions of x.

ax-bx%2Ba=1

%28a-b%29x%2Ba=1

Be reminded, EXPRESSIONS of x...

%28a-b%29x%2Ba=0%2Ax%2B1
Compare the corresponding parts to build a simple system of equations.
-
system%28a-b=0%2Ca=1%29


Not yet solved for both a and b, but you can now see how to finish.