Mathematics

# Resolve into partial fractions :$\dfrac{7+x}{(1+x)(1+x^{2})}$

##### SOLUTION
Let, $\dfrac{7 + x}{(1 + x)(1 + x^2)} = \dfrac{A}{1+x} + \dfrac{Bx + C}{1+x^2}$

$\implies \dfrac{7 + x}{(1 + x)(1 + x^2)} = \dfrac{A(1+x^2) + (Bx + C)(1+x)}{(1+x)(1+x^2)}$

$\implies 7 + x = A + Ax^2 + Bx + Bx^2 + C + Cx$

$\implies 7 + x = (A+B)x^2 + (B+C)x + (A+C)$

i.e., $A + B = 0$...........(i)
$B + C = 1$
and $A + C = 7$

$\implies A - B = 6$........(ii)

By (i) & (ii) we get, $A = 3, B = - 3$  and $C = 4$

$\therefore \dfrac{7 + x}{(1 + x)(1 + x^2)} = \dfrac{3}{1+x} + \dfrac{- 3x + 4}{1+x^2}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

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