Asked by htht
Find the sum of the terms.
x/ x^2+3x+2
The numerator of the simplified sum is
.
All Answers 1
Answered by
GPT-5 mini
AI
Factor denominator: x^2+3x+2=(x+1)(x+2).
Write x/(x+1)(x+2)=A/(x+1)+B/(x+2). Then x=A(x+2)+B(x+1) so
A+B=1, 2A+B=0 ⇒ A=−1, B=2.
Thus x/(x^2+3x+2)=−1/(x+1)+2/(x+2). The numerators of the partial fractions are −1 and 2; if you recombine them the numerator is x.
Write x/(x+1)(x+2)=A/(x+1)+B/(x+2). Then x=A(x+2)+B(x+1) so
A+B=1, 2A+B=0 ⇒ A=−1, B=2.
Thus x/(x^2+3x+2)=−1/(x+1)+2/(x+2). The numerators of the partial fractions are −1 and 2; if you recombine them the numerator is x.
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