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Alex787 [66]
3 years ago
13

Review the work showing the first few steps in writing a partial fraction decomposition.

Mathematics
2 answers:
Amanda [17]3 years ago
6 0

Answer:

A = 2

B = -1

C = -9

Step-by-step explanation:

Given

2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C

Required

Find A, B and C

Rearrange the expression

2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C

2x\² + 15x + 19 = Ax\² + 8Ax + Bx + 16A + 4B + C

To do this, we simply compare the expressions on both sides of the equation.

So, we have:

Ax\² = 2x\² --- (1)

8Ax + Bx = 15x --- (2)

16A + 4B + C = 19 --- (3)

Divide both sides by x² in (1)

Ax\² = 2x\²

A = 2

Divide both sides by x in (2)

8Ax + Bx = 15x

8A + B = 15

Substitute 2 for A.

8*2 + B = 15

16+ B = 15

Make B the subject

B = 15 - 16

B = -1

Substitute 2 for A and -1 for B in (3)

16A + 4B + C = 19

16*2 + 4*-1 + C = 19

32 - 4 + C = 19

28 + C = 19

Make C the subject

C = 19 - 28

C = -9

GalinKa [24]3 years ago
4 0

Answer:

Option-3

Step-by-step explanation:

edge

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