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SOLUTION: I am having the hardest time with this. Solve by the method of your choice: (1/x^2-3x+2)=(1/x+2)+(5/x^2-4) I have tried this different ways and just cant figure it out.
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-> SOLUTION: I am having the hardest time with this. Solve by the method of your choice: (1/x^2-3x+2)=(1/x+2)+(5/x^2-4) I have tried this different ways and just cant figure it out.
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Question 537580
:
I am having the hardest time with this. Solve by the method of your choice:
(1/x^2-3x+2)=(1/x+2)+(5/x^2-4)
I have tried this different ways and just cant figure it out.
Found 2 solutions by
bucky, Tatiana_Stebko
:
Answer by
bucky(2189)
(
Show Source
):
You can
put this solution on YOUR website!
Although you wrote (according to the rules of algebra) that you were given to solve:
.
.
I'm guessing that you really were to solve the following:
.
.
If I'm wrong I apologize, and please ignore the following and re-submit your problem.
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Start with:
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Where it is possible, factor the denominators. This will give you:
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Next, multiply both sides (all terms) by the three factors common to the denominator. Just multiply each of the terms on both sides by:
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When you do that the equation becomes:
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Now in each term cancel any factors that are in both the numerator and the denominator:
.
.
and you are left with:
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Multiply out the two terms on the right side to get:
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On the right side combine the -3x and +5x to get +2x. Also combine the +2 and the -5 to get -3. This reduces the equation to:
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Then get everything on one side of the equation by subtracting x + 2 from both sides. The equation then becomes:
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Transpose it to the standard quadratic form:
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Solve by using the quadratic formula:
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Recall that a is the multiplier of the
. Therefore, a = 1. b is the multiplier of the x. Therefore b also = 1. And c is the constant. And so c = -5. Substituting these values into the quadratic formula results in:
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This becomes:
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So the two answers for x are:
.
.
and
.
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Hope this helps you to clear up the places you had trouble with.
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Answer by
Tatiana_Stebko(1470)
(
Show Source
):
You can
put this solution on YOUR website!
The fraction is equal 0 when the numerator is equal 0 and denominator is not equal 0
multiply by -1
Use the quadratic formula
,
,