Question 1.39: Express 2x+5/x²+2x+1 as partial fractions...
Express
\frac{2 x+5}{x^2+2 x+1}as partial fractions
Step-by-Step
The denominator is factorized to give (x + 1)² . Here we have a case of a repeated factor.
This repeated factor generates partial fractions \frac{A}{x+1}+\frac{B}{(x+1)^2}. Thus
Multiplying by (x + 1)² gives
2 x+5=A(x+1)+B=A x+A+BEquating coefficients of x gives A = 2. Evaluation with x = — 1 gives B = 3. So
\frac{2 x+5}{x^2+2 x+1}=\frac{2}{x+1}+\frac{3}{(x+1)^2}Related Answered Questions
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