# BHARDWAJ CLASSES

## What are Partial Fraction?

As we can know we can do this
. $9 x+4 + 2 x−1 = 11x−1 ( x+4 ) ( x−1 )$
like this
$9 x+4 + 2 x−1 = 9(x+1)+2(x+4) ( x+4 )(x−1) = 9x−9+2x+8 ( x+4 )( x−1 ) = 11x−1 ( x+4 )( x−1 )$
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) ).

$11x−1 ( x+4 )( x−1 ) = A ( x+4 ) + B ( x−1 )$

Step 3  Multiply through by the bottom so we no longer have fractions
$11x−1 = A( x−1 ) + B( x+4 )$

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