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Polynomials

Question

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Insert three rational numbers between $negative 2 over 5 space and space minus 1 fifth$

Solution

fraction numerator open parentheses negative begin display style 2 over 5 end style close parentheses plus open parentheses negative begin display style 1 fifth end style close parentheses over denominator 2 end fraction equals negative 3 over 10 fraction numerator open parentheses negative begin display style 2 over 5 end style close parentheses plus open parentheses negative begin display style 3 over 10 end style close parentheses over denominator 2 end fraction equals fraction numerator open parentheses negative begin display style 7 over 10 end style close parentheses over denominator 2 end fraction equals negative 7 over 20 fraction numerator open parentheses negative begin display style 3 over 10 end style close parentheses plus open parentheses negative begin display style 1 fifth end style close parentheses over denominator 2 end fraction equals fraction numerator open parentheses negative begin display style 3 over 10 end style close parentheses plus open parentheses negative begin display style 2 over 10 end style close parentheses over denominator 2 end fraction equals space fraction numerator open parentheses negative begin display style 5 over 10 end style close parentheses over denominator 2 end fraction equals negative 5 over 20 equals negative 1 fourth

Thus, three rational numbers which can be inserted between

negative 2 over 5 space and space minus 1 fifth space are space minus 7 over 20 comma space minus 3 over 10 space and space minus 1 fourth.

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