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Easy

Question

The number of partial fractions of  fraction numerator 2 over denominator x to the power of 4 plus x squared plus 1 end fraction

  1. 2    
  2. 3  
  3. 4    
  4. 5    

The correct answer is: 2



    fraction numerator 2 over denominator x to the power of 4 plus x squared plus 1 end fraction
equals fraction numerator 2 over denominator open parentheses x squared plus x plus 1 close parentheses open parentheses x squared minus x plus 1 close parentheses end fraction
equals fraction numerator A x plus B over denominator open parentheses x squared plus x plus 1 close parentheses end fraction plus fraction numerator C x plus D over denominator open parentheses x squared minus x plus 1 close parentheses end fraction
w h e r e
fraction numerator A x plus B over denominator open parentheses x squared plus x plus 1 close parentheses end fraction space space space space..... open parentheses 1 close parentheses
fraction numerator C x plus D over denominator open parentheses x squared minus x plus 1 close parentheses end fraction space space space space space.... open parentheses 2 close parentheses

H e n c e comma space t h e space n u m b e r space o f space p a r t i a l space f r a c t i o n s space o f space fraction numerator 2 over denominator x to the power of 4 plus x squared plus 1 end fraction space a r e space 2.

    Partial fractions are the fractions used for the decomposition of a rational expression. When an algebric expression is split into a sum of two or more rational expressions, then each part is called a partial fraction.

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