MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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10.7 Partial Fractions

Focus on partial fractions and proper rational expression.

Before you solve

Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Distinct linear factorsWorked steps · five questions02Repeated and quadratic factorsWorked steps · five questions
Lesson brief and rules

10.7 Partial Fractions

For distinct linear factors, write Ax−a+Bx−b\frac{A}{x-a}+\frac{B}{x-b} and solve for A,BA,B.

Worked example 11
01 / Decompose 3(x−1)(x−2)\dfrac{3}{(x-1)(x-2)}.
02 / A(x−2)+B(x−1)=3A(x-2)+B(x-1)=3; at x=1,A=−3x=1, A=-3; at x=2,B=3x=2, B=3.
03 / Answer: −3x−1+3x−2-\dfrac{3}{x-1}+\dfrac{3}{x-2}
Worked example 2 · Proper rational expression

Is x+1x2+4\dfrac{x+1}{x^{2}+4} proper?

Numerator degree 11 is less than denominator degree 22. Answer: Yes

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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