Question 130061
I have a word problem that I'm not sure if I've solved correctly, could I have some help please. thank you. The reciprocal of a number plus the reciprocal of three times the number equals 1/3. Find the number. I have x+3x=1/3 x=1/12. Is this correct?
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No I'm afraid it isn't.  "Reciprocal of" means "one over"

{{{1/x + 1/(3x)=1/3}}}

Enclose every term in parentheses:

{{{(1/x) + (1/(3x))=(1/3)}}}

Clear of fractions:
Multiply thru by LCD = {{{3x}}}  written as {{{((3x)/1)}}}

{{{((3x)/1)(1/x) + ((3x)/1)(1/(3x))=((3x)/1)(1/3)}}}

Now we cancel:

{{{((3cross(x))/1)(1/cross(x)) + ((cross(3)cross(x))/1)(1/(cross(3)cross(x)))=((cross(3)x)/1)(1/cross(3))}}}

{{{3 + 1 = x}}}

{{{4 = x}}}

Edwin</pre>