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How does this (-x -6) / (x2 + 3x)

Simplify to: 1/(x+3) - (2/x)

 Aug 6, 2017
 #1
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y = (-x-6)/(x2+3x) 

 

y = (-x-6)/(x(x+3))

 

Use partial fraction expansion:

 

y = A/x  +  B/(x+3)

y = (A(x+3) + Bx)/(x(x+3)) → ((A+B)x + 3A)/(x(x+3))

 

For the two sets of y to be the same we must have:

 

3A = -6  so  A = -2

 

A + B = -1

-2 + B = -1 so B = 1

 

Hence y = -2/x + 1/(x+3)

.

 Aug 6, 2017

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