SOLUTION: Write the rational expression 7/2x^2-5x-3 as a sum of partial fractions.

Question 600952: Write the rational expression 7/2x^2-5x-3 as a sum of partial fractions.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write the rational expression 7/2x^2-5x-3 as a sum of partial fractions.
Factor the denominator and write it
= +
:
Combine the fractions on the right
=
:
If the denominators are equal, the numerators are, we can write it
7 = A(x-3) + B(2x+1)
:
Assume this is an identity, equation true for all values of x.
Let x=3
7 = A(3-3) + B(2(3)+1)
The A term drops out
7 = 7B + 0
B = 1
:
Let x=-.5
7 = A(-.5-3) + B(2(-.5)+1)
The B term drops out
7 = -3.5A + 0
A = -2
:
The decomposed fraction
= +

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