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Mapel : Matematika
Bab : Sistem Persamaan Linear Dua Variabel (SPLDV)

 5/x - 3/y = 1
7/x + 3/y = 2
-----------------  +
       12/x = 3
            x = 12/3
            x = 4

5/x - 3/y = 1
5/4 - 3/y = 1
      - 3/y = 1 - 5/4
      - 3/y = 4/4 - 5/4
      - 3/y = -1/4
           y = 4 x (-3) : (-1)
           y = 12

1/x - 1/y
= 1/4 - 1/12
= 3/12 - 1/12
= 2/12
= 1/6

[tex] \frac{5}{x} - \frac{3}{y}=1 \\ \\ \frac{7}{x} + \frac{3}{y}=2 \\ -----(+) \\ \\ \frac{5}{x} + \frac{7}{x}=1+2 \\ \\ \frac{12}{x}=3 \\ \\ 12=3x \\ \\x= \frac{12}{3} \\ \\ x=4 [/tex]

Masukan nilai x ke persamaan pertama:

[tex] \frac{5}{x} - \frac{3}{y}=1 \\ \\ \frac{5}{4} - \frac{3}{y}=1 \\ \\ -\frac{3}{y}=1- \frac{5}{4} \\ \\ -\frac{3}{y}=\frac{4}{4}- \frac{5}{4} \\ \\ -\frac{3}{y}=- \frac{1}{4} \\ \\y=( -\frac{4}{1}).(-3) \\ \\ y= 12 [/tex]

Masukan nilai x dan y ke pertanyaan soal

[tex]= \frac{1}{x} - \frac{1}{y} \\ \\ = \frac{1}{4} - \frac{1}{12} \\ \\= \frac{3}{12} - \frac{1}{12} \\ \\= \frac{2}{12}= \frac{1}{6} .......... Jawaban\ (D)[/tex]