Solve the following by using rational algebraic expressions.
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Solve the following by using rational algebraic expressions.
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a number = x
thrice another number = 3x
the sum of their reciprocal is equal to 4
1/x + 1/3x = 4
LCD = 3x
3x (1/x + 1/3x = 4)
3x/x + 3x/3x = 3x(4)
3 + 1 = 12x
4 = 12x
4/12 = x
1/3 = x
Let the first number be
, then the other number is
and their reciprocals are
and
.
Thus,
.
Multiplying through by the Least Common Denominator (LCD), which is
, we have 
Thus, the first number is
and the other number is
.
Therefore, the numbers are
and 1.