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The sum of the reciprocals of two consecutive even integers is 9/40. This can be represented by the equation shown.1/x + 1/x+2 = 9/40

The sum of the reciprocals of two consecutive even integers is 9/40. This can be represented-example-1
User Ricree
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Step-by-step explanation


(1)/(x)+(1)/(x+2)=(9)/(40)

Adding the two fractions:


(x+2+x)/(x(x+2))=(9)/(40)
(2x+2)/(x^2+2x)=(9)/(40)

We subtract 9/40 to equal zero:


(2x+2)/(x^(^2)+2x)-(9)/(40)=0

Subtracting the two fractions:


(40(2x+2)-9(x^2+2x))/(40(x^2+2x))=0
(80x+80-9x^2-18x)/(40x^2+80x)=0
(-9x^2+62x+80)/(40x^2+80x)=0

Factoring:


(-(9x+10)(x-8))/(40x(x+2))=0

This equation is zero when:


\begin{gathered} 9x+10=0 \\ 9x=-10 \\ x=-(10)/(9) \end{gathered}

or


\begin{gathered} x-8=0 \\ x=8 \end{gathered}

The only integer solution is x=8.


\begin{gathered} (1)/(8)+(1)/(10)=(10+8)/(80)=(18)/(80)=(9)/(40) \\ \\ \frac{}{} \\ \end{gathered}

Answer

x=8

User Sian
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