In this worksheet, we will practice decomposing rational expressions into partial fractions when the denominator has nonrepeated linear factors.

Q1:

Express 𝑥−2(𝑥+2)(𝑥−3)(𝑥+1) in partial fractions.

Q2:

Find 𝐴 and 𝐵 such that 4𝑥−2(𝑥+3)(𝑥−2)=𝐴𝑥+3+𝐵𝑥−2.

Q3:

Express 𝑥−2𝑥(𝑥−3) in partial fractions.

Q4:

The expression 2𝑥+1(𝑥+2)(𝑥+3) can be written in the form 𝐴𝑥+3+𝐵𝑥+2. Find the values of 𝐴 and 𝐵.

Q5:

Find 𝐴 and 𝐵 such that 4(𝑥+8)(𝑥−2)=𝐴𝑥−2+𝐵𝑥+8.

Q6:

Mason wants to convert the rational expression 6𝑥+5𝑥−45𝑥+6𝑥 into partial fractions.

His first step is to divide the numerator by the denominator. Complete this division.

Mason now converts this expression into partial fractions. Convert the expression into partial fractions.

Q7:

Convert the rational expression 6𝑥−2𝑥+5𝑥+4𝑥+3 into partial fractions.

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