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Basic of Logarithms
easy
The partial fraction of ${{6{x^4} + 5{x^3} + {x^2} + 5x + 2} \over {1 + 5x + 6{x^2}}} = $
A
${x^2} + {1 \over {1 + 2x}} + {1 \over {1 + 3x}}$
B
${x^2} - {1 \over {1 + 2x}} + {1 \over {1 + 3x}}$
C
${x^2} + {1 \over {1 + 2x}} - {1 \over {1 - 3x}}$
D
None of these
Solution
(a) ${{6{x^4} + 5{x^3} + {x^2} + 5x + 2} \over {6{x^2} + 5x + 1}} = {{{x^2}(6{x^2} + 5x + 1) + (5x + 2)} \over {(6{x^2} + 5x + 1)}}$
= ${x^2} + {{5x + 2} \over {(2x + 1)\,(3x + 1)}} = {x^2} + {{(2x + 1)\, + \,(3x + 1)} \over {(2x + 1)\,(3x + 1)}}$
= ${x^2} + {1 \over {2x + 1}} + {1 \over {3x + 1}}$.
Standard 11
Mathematics
