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08-03-2021
Mathematics

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express (5x+3)/((2x-3)(x+2)) in partial fractions

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08-03-2021

Answer:

(5x+3)/((2x-3)(x+2)) = 3/(2x-3)+1/(x+2)

Step-by-step explanation:

Let

(5x+3)/((2x-3)(x+2)) = A/(2x-3)+B/(x+2)

5x+3=A(x+2)+B(2x-3)

5x+3=x(A+2B)+(2A-3B)

comparing x:

5=A+2B ... (1)

comparing constant:

3=2A-3B ... (2)

By solving:

A=3, B=1

(5x+3)/((2x-3)(x+2)) = 3/(2x-3)+1/(x+2)

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