Step-by-step explanation:
As the sum of the reciprocals of the two positive integers is frac 3/16
So,
[tex]\frac{1}{x}\:+\:\frac{1}{2x}\:=\:\frac{3}{16}[/tex]
[tex]\mathrm{Multiply\:by\:LCM=}16x[/tex]
[tex]\frac{1}{x}\cdot \:16x+\frac{1}{2x}\cdot \:16x=\frac{3}{16}\cdot \:16x[/tex]
Simplify
[tex]24=3x[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]3x=24[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]
[tex]\frac{3x}{3}=\frac{24}{3}[/tex]
[tex]x=8[/tex]
So,
[tex]2x=16[/tex]
[tex]\frac{1}{8}\:+\:\frac{1}{16}[/tex]
[tex]\mathrm{Least\:Common\:Multiplier\:of\:}8,\:16:\quad 16[/tex]
[tex]=\frac{2}{16}+\frac{1}{16}[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{2+1}{16}[/tex]
[tex]=\frac{3}{16}[/tex]
Therefore,
[tex]\frac{1}{8}+\frac{1}{16}=\frac{3}{16}[/tex]
Keywords: word problem , integer
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