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Wednesday, September 13, 2017

Partial Fraction

introduction of partial fraction


What are Partial Fraction?








As we can know we can do this
                                            . 9 x+4 + 2 x1 = 11x1 ( x+4 )( x1 )
like this
9 x+4 + 2 x1 = 9(x+1)+2(x+4) ( x+4 )(x1) = 9x9+2x+8 ( x+4 )( x1 ) = 11x1 ( x+4 )( x1 )
but how can we do the reverse?

That process is known as Partial Fraction.

So now let we see how to do this.
        

Step 1    factor the denominator

in our example denominator is already in factorized form

Step 2  Take  two constants A & B (because in denominator we have two factor i.e. (x + 4), (x - 1) ).

11x1 ( x+4 )( x1 ) = A ( x+4 ) + B ( x1 )

Step 3  Multiply through by the bottom so we no longer have fractions
11x1=A( x1 )+B( x+4 )

Step 4  Now find the value of constants( i.e. A & B)
                 Substituting the roots, or "zeros", of  (x + 4) & (x - 1)
forx1=0x=1 11( 1 )1=A( 1-1 )+B( 1+4 ) 10=A( 0 )+B( 5 ) B=2 Againx+4=0x=4 11( 4 )1=A( -4-1 )+B( 4+4 ) 45=A( 5 )+B( 0 ) A=9
NOW THIS IS OUR ANSWER 11x1 ( x1 )( x+4 ) = 9 ( x+4 ) + 2 ( x1 )

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