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 $$C = 4$$

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

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
What is the value of the expression $$\dfrac{{\cos \left( {{{90}^0} + \theta } \right)\sec \left( { - \theta } \right)\tan \left( {{{180}^0} - \theta } \right)}}{{\sec \left( {{{360}^0} - \theta } \right)\sin \left( {{{180}^0} + \theta } \right)\cot \left( {{{90}^0} - \theta } \right)}} \ \ \ ? $$
  • A. $$\pi$$
  • B. $$\frac { \pi } { 2 }$$
  • C. $$0$$
  • D. $$-1$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Solve:
$$\int\limits_0^1 {{{\tan }^{ - 1}}\left( {\dfrac{{2x}}{{1 - {x^2}}}} \right)dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Find the integral of    $$\displaystyle \int \frac {x^3+3x+4}{\sqrt x}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Hard
Evaluate
$$\int \dfrac {x^{7}}{(1+x^{4})^{2}}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Solve $$\displaystyle\int {\frac{{{x^5}}}{{{x^2}\, + \,9}}} \,dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer