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Excel in math and science
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Algebra
Partial Fractions
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
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Concept Quizzes
If the following is an identity in \(x\): \[\frac{4x^2+27x+33}{(x-1)(x+3)^2}=\frac{a}{x-1}+\frac{bx+c}{(x+3)^2},\] what is the value of \(a+b+c\)?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
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by Brilliant Staff
Suppose \(a\), \(b\), and \(c\) are constants such that the following holds for all real numbers \(x\) such that all of the denominators are nonzero:
\[\frac{9}{x(x+1)^2}=\frac{a}{x}+\frac{b}{x+1}+\frac{c}{(x+1)^2}.\] What is the value of \(abc?\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
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by Brilliant Staff
If the following is an identity in \(x\): \[\frac{17x^3+7x^2-17x-7}{(x-1)^2(x+1)^2}=\frac{A}{x-1}+\frac{B}{x+1},\] what is the value of \(A \times B?\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
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by Brilliant Staff
If the following is an identity in \(x\): \[\frac{11x^2+90x+99}{(x-3)^2(x+3)^2}=\frac{A}{(x-3)^2}-\frac{B}{(x+3)^2},\] what is the value of \(A \times B?\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
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If the following is an identity in \(x\): \[\frac{-13x+32}{(x+1)(x-2)^2}=\frac{a}{x+1}+ \frac{ b} { (x-2) } + \frac{ c} { (x-2)^2} , \] what is the value of \(a+b+c\)?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
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by Brilliant Staff