Question 5 5 pts The fraction $$ \frac{ax^3+bx^2+cx+d}{(x^2+1)(x^2-4)} $$ will take which form when expressed as partial fractions? $$ \frac{Ax+B}{x^2+1} + \frac{Cx+D}{x^2-4} $$ $$ \frac{A}{x^2+1} + \frac{B}{x+2} + \frac{C}{x-2} $$ $$ \frac{Ax+B}{x^2+1} + \frac{C}{x^2-4} $$ $$ \frac{Ax+B}{x^2+1} + \frac{C}{x+2} + \frac{D}{x-2} $$
Added by Remedios M.
Close
Step 1
We need to express this fraction in partial fractions. First, factor the denominator completely. The term $$(x^2+1)$$ is an irreducible quadratic factor over real numbers because its discriminant is $0^2 - 4(1)(1) = -4 < 0$. The term $$(x^2-4)$$ is a difference Show more…
Show all steps
Your feedback will help us improve your experience
Khushbu Rani and 83 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The fraction (x^2 + 1)/(x^2 - 4) will take which form when expressed as partial fractions?
Khushbu R.
Q3) If we want to decompose x^2 + 4x + 5 / (x^2 - 1)^2(x^2 + 2x + 5) into partial fractions, we should look for an expression in the form:
Madhur L.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD