SOLUTION: Write 3x-1/x+1 in a form a/x+1 +b state the values of a and b

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Question 1007414: Write 3x-1/x+1 in a form a/x+1 +b state the values of a and b
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You might really mean this:
(3x-1)/(x+1) in a form a/(x+1)+b

Not the same as what you wrote.


Better notation will resemble the two forms, %283x-1%29%2F%28x%2B1%29 and a%2F%28x%2B1%29%2Bb.

Begin with the second form, the one using two terms, and combine into a single rational expression.

a%2F%28x%2B1%29%2Bb%28%28x%2B1%29%2F%28x%2B1%29%29

a%2F%28x%2B1%29%2B%28bx%2Bb%29%2F%28x%2B1%29

%28a%2Bbx%2Bb%29%2F%28x%2B1%29

highlight_green%28%28bx%2Ba%2Bb%29%2F%28x%2B1%29%29, and this is comparable in form to the first given rational expression. Now the comparison of corresponding expressions or variables and numbers gives you:
system%28bx=3x%2C-1=a%2Bb%29

and simpler system%28b=3%2Ca%2Bb=-1%29-----b is obvious, and solving for a is simple. a=-4.