SOLUTION: Resolve 7-8x/(1-x)*(2-x)into partial fractions.Hence find the expansion of the function in ascending powers of x as far as three nonzero terms. State for which values of x this exp

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Resolve 7-8x/(1-x)*(2-x)into partial fractions.Hence find the expansion of the function in ascending powers of x as far as three nonzero terms. State for which values of x this exp      Log On


   

Question 97394: Resolve 7-8x/(1-x)*(2-x)into partial fractions.Hence find the expansion of the function in ascending powers of x as far as three nonzero terms. State for which values of x this expansion is valid

I need this answer,today.Please.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%287-8x%29%2F%28%281-x%29%282-x%29%29 Start with the given expression


%287-8x%29%2F%28%281-x%29%282-x%29%29=A%2F%281-x%29%2BB%2F%282-x%29 Break up the fraction into two smaller fractions


Multiply both sides by the LCD %281-x%29%282-x%29. This will eliminate any fractions.



Distribute. Notice the denominators cancel.


7-8x=A%282-x%29%2BB%281-x%29 Simplify


Now to find A, simply eliminate B. So to eliminate B, let x=1



7-8%281%29=A%282-1%29%2BB%281-1%29 plug in x=1

7-8=A%282-1%29%2BB%281-1%29 multiply


-1=A%281%29%2BB%280%29 Combine like terms



-1=A Multiply



So our first value is A=-1


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Now to find B, simply eliminate A. So to eliminate A, let x=2



7-8%282%29=A%282-2%29%2BB%281-2%29 plug in x=2


7-16=A%282-2%29%2BB%281-2%29 multiply


-9=A%280%29%2BB%28-1%29 Combine like terms

-9=-B Multiply and combine like terms

9=B Divide both sides by -1


So our second value is B=9



So our values are A=-1 and B=9



So that means %287-8x%29%2F%28%281-x%29%282-x%29%29=-1%2F%281-x%29%2B9%2F%282-x%29 where x%3C%3E1 or x%3C%3E2



Check:


To verify the answer, simply compare the graphs of the original expression and the answer. You'll see that they are equivalent, so that verifies your answer.