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,

$\frac{6}{x-2}-\frac{5}{x+2}=5(\frac{1}{x^2-4})$

On solving we get,

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

Hence, the value of x is -17.