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Calculus/Partial Fractions

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Expert: - 11/4/2008


Question
Hey,
I'm a first year Natural Science undergrad at Cambridge University, and I'm having an absolute nightmare trying to split the following into partial fractions...

1/(Y(K-Y))

(Its part of an integration problem where I have to integrate the above with respect to y)

Any help would be much appreciated as for some reason this has got me ripping my hair out!

Many Thanks,
Dan.

Answer
The two fractions are of the form A/Y and B/(K-Y).
The way to find what they are is to set 1/(Y(K-Y)) = A/Y + B/(K-Y) .

To find what A and B are, we need everything over one denominator on the right side of the equation (just like on the left).

To do this, multiply A/Y by (K-Y)/(K-Y) and B/(K-Y) by Y/Y.

You can now combine both terms into a common fraction on the right side of the equation

You will get an A(K-Y) + BY on top of the fraction that now shares the same denominator as the left hand side of the equation.

Multiply it out, giving AK - AY + BY and set the equal to 1.
Note that what has to be done is to set AK = 1 and then -AY + BY = 0.

A can be found, and then B (since K is a constant like any other number).  

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