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Excel in math and science
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Algebra
Partial Fractions
Excel in math and science
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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 \(x\): \[\frac{9x^2+9}{x^3+1}=\frac{a}{x+1}+\frac{bx+c}{x^2-x+1},\] 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
If the following is an identity in \(x\): \[\frac{10x^2+1}{x(x^2+1)}=\frac{a}{x}+\frac{bx+c}{x^2+1},\] 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
If the following is an identity in \(x\): \[\frac{9x-4}{x^3-2x+1}=\frac{a}{x-1}+\frac{bx+c}{x^2+x-1},\] what is the value of \(a \times b \times c\)?
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,
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If the following is an identity in \(x\): \[\frac{5x^2+Ax+B}{(7x+1)(x^2-7x+1)}=C\left(\frac{1}{7x+1}+\frac{1}{x^2-7x+1}\right),\] 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,
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Which of the following is the partial fraction decomposition of
\[ \frac{ 1} { x^3 + x } ? \]
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,
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Used and loved by 4 million people
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including olympiad champions, researchers, and professionals.
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That seems reasonable.
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by Brilliant Staff