Question

Six divided by the difference if a number and 2 minutes 5 divided by a number plus 2, equals 5 times the reciprocal of the difference of the number squared and 4 what is the number ? The number is ?

Answer 1

Let us frame the equation as follows,

Let the unknown number be x.

So, we have,

`(6)/(x-2)-(5)/(x+2)=5((1)/(x^2-4))`

On solving we get,

`\begin{gathered} (6\mleft(x+2\mright)-5(x-2))/((x-2)(x+2))=(5)/(x^2-4) \\ (6x+12-5x+10)/((x-2)(x+2))=(5)/((x-2)(x+2)) \\ 6x+12-5x+10=5 \\ x+22=5 \\ x=-17 \end{gathered}`

Hence, the value of x is -17.