`(x^2 + 5)/((x + 1)(x^2 - 2x + 3))` Write the partial fraction decomposition of the rational expression. Check your result algebraically.

Expert Answers

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equating the coefficients of the like terms,




Now let's solve the above three equations to find the values of A,B and C,

Express C in terms of A from the third equation,


Substitute the above expression of C in second equation,




Now subtract the first equation from the above equation,




Plug the value of A in the first and third equation to get the values of B and C,








Now let's check it algebraically,




Hence it is verified.

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