Pertanyaan

1 + x b − a 1 + 1 + x a − b 1 = ...

$\frac{1}{1 + x ^{b - a}} + \frac{1}{1 + x ^{a - b}} = ...$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D

Pembahasan

Ingat kembali: Sehingga, kita peroleh perhitungan: Dengan demikian, hasil dari adalah Jadi, jawaban yang tepat adalah D

Ingat kembali:

a to the power of m times a to the power of n equals a to the power of m plus n end exponent. space a not equal to 0

a to the power of 0 equals 1 comma space a not equal to 0

$1 over a plus 1 over b equals fraction numerator b plus a over denominator a times b end fraction comma space a space dan space b not equal to 0$

open parentheses 1 plus a close parentheses open parentheses 1 plus b close parentheses equals 1 plus a plus b plus a b

Sehingga, kita peroleh perhitungan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator 1 plus x to the power of b minus a end exponent end fraction plus fraction numerator 1 over denominator 1 plus x to the power of a minus b end exponent end fraction end cell equals cell fraction numerator 1 plus x to the power of a minus b end exponent plus 1 plus x to the power of b minus a end exponent over denominator open parentheses 1 plus x to the power of b minus a end exponent close parentheses open parentheses 1 plus x to the power of a minus b end exponent close parentheses end fraction end cell row blank equals cell fraction numerator 2 plus plus x to the power of a minus b end exponent plus x to the power of b minus a end exponent over denominator 1 plus x to the power of a minus b end exponent plus x to the power of b minus a end exponent plus open parentheses x to the power of a minus b end exponent close parentheses times open parentheses x to the power of b minus a end exponent close parentheses end fraction end cell row blank equals cell fraction numerator 2 plus plus x to the power of a minus b end exponent plus x to the power of b minus a end exponent over denominator 1 plus x to the power of a minus b end exponent plus x to the power of b minus a end exponent plus x to the power of a minus b plus b minus a end exponent end fraction end cell row blank equals cell fraction numerator 2 plus plus x to the power of a minus b end exponent plus x to the power of b minus a end exponent over denominator 1 plus x to the power of a minus b end exponent plus x to the power of b minus a end exponent plus x to the power of 0 end fraction end cell row blank equals cell fraction numerator 2 plus plus x to the power of a minus b end exponent plus x to the power of b minus a end exponent over denominator 1 plus x to the power of a minus b end exponent plus x to the power of b minus a end exponent plus 1 end fraction end cell row blank equals cell fraction numerator 2 plus plus x to the power of a minus b end exponent plus x to the power of b minus a end exponent over denominator 2 plus x to the power of a minus b end exponent plus x to the power of b minus a end exponent end fraction end cell row blank equals 1 end table$

Dengan demikian, hasil dari $fraction numerator 1 over denominator 1 plus x to the power of b minus a end exponent end fraction plus fraction numerator 1 over denominator 1 plus x to the power of a minus b end exponent end fraction$ adalah

Jadi, jawaban yang tepat adalah D