Number and Algebra
Functions
Geometry & Trigonometry
Statistics & Probability
Calculus
Find the partial fraction decomposition of 4x+7x2+3x+2\displaystyle \frac{4x+7}{x^2 + 3x +2}x2+3x+24x+7.
Decompose the rational expression 2x+3x2−x−2\displaystyle \frac{2x+3}{x^2 - x - 2}x2−x−22x+3 into partial fractions.
Express 3x−1(x+2)(x−3)\displaystyle \frac{3x-1}{(x+2)(x-3)}(x+2)(x−3)3x−1 in partial fractions.
Simplify and decompose into partial fractions: x2−4x3−x\displaystyle \frac{x^2 -4}{x^3 - x}x3−xx2−4.
Express x2+1(x−2)2\displaystyle \frac{x^2 +1}{(x-2)^2}(x−2)2x2+1 in partial fractions.
Decompose 2x2+3x+4(x−1)(x2+1)\displaystyle \frac{2x^2 +3x +4}{(x-1)(x^2+1)}(x−1)(x2+1)2x2+3x+4 into partial fractions.
Decompose into partial fractions: x2+2x+5x3+x2−x−1\displaystyle \frac{x^2 + 2x +5}{x^3 + x^2 - x -1}x3+x2−x−1x2+2x+5.
Perform partial fraction decomposition on 2x3+5x2+x+3x2−4\displaystyle \frac{2x^3 +5x^2 +x +3}{x^2 -4}x2−42x3+5x2+x+3.
Decompose 3x2−3x+4(x2+3)(x−1)\displaystyle \frac{3x^2 -3x +4}{(x^2+3)(x-1)}(x2+3)(x−1)3x2−3x+4 into partial fractions.
Decompose 4x2+2x+1(x−3)2(x+2)\displaystyle \frac{4x^2 +2x +1}{(x-3)^2(x+2)}(x−3)2(x+2)4x2+2x+1 into partial fractions.
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Question Type 2: Applying partial fractions on linear factors on higher powers
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