Page 29 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II

Notes Method 3:
Verify at x near infinity

Self Assessment

Fill in the blanks:
8. After having determined the right outline for the partial fraction decomposition of a
rational function, we are required to calculate the ............................. coefficient.

9. The method that uses the constant, linear, quadratic or higher approximation is known as
............................. .
10. Assess both sides of equation (*) at r points where r is the number of unidentified coefficients
is included in ............................. method.

2.3 Partial Fractions

Every proper rational fraction cab be expressed as a sum of simple fractions whose denominators
2
n
n
are of the form (9x+b) and (9x +bx+c) , n being a positive integer.
2.3.1 Distinct Linear Factors
To each linear factor ax+b occurring once in the denominator of a proper rational fraction, there
A
corresponds a single partial fraction of the form , where A is a constant to the determined.

ax b
2.3.2 Repeated Linear Factors

To each linear factors ax+b occurring n times in the denominator of a proper rational fraction.
These corresponds a sum of n partial fractions of the form.

A A A
1  2       n
ax  b ax b  2 ax b  n


where the A’s are constants to be obtained of course A n  0

2.3.3 Distinct Quadratic Factors

2

To each irreducible quadratic factor ax  bx c occurring once in the denominator of a proper

Ax B
rational fraction, there corresponds a simple partial fraction of the form 2 where A

9x  bx c
and b are constants to be determined.

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