Question 443818
<br>
This is a funny question. I wonder what is the purpose of it.
Let this jumpy number be called x!
Then translating the problem statement using algebraic symbols for operators and x for "a number" we have the following:
7/(x-2) - 6/(x+2) = 6*1/(x<sup>2</sup>-4). What is x?<br>
Note that the denominators in three fractions are (x-2), (x+2) and (x<sup>2</sup>-4). Also, note that (x<sup>2</sup>-4) = (x-2)*(x+2).<br>
After multiplying both sides of the equation by (x<sup>2</sup>-4), we have:
7(x<sup>2</sup>-4)/(x-2) - 6(x<sup>2</sup>-4)/(x+2) = 6(x<sup>2</sup>-4)/(x<sup>2</sup>-4), which becomes:
7(x-2)(x+2)/(x-2) - 6(x-2)(x+2)/(x+2) = 6, which is the same as
7(x+2) - 6(x-2) = 6<br>
After expanding the brackets:
7x + 14 - 6x + 12 = 6<br>
After simplifying the left hand side:
x + 26 = 6<br>
After taking away 26 from both sides of the equation:
x = -20.<br>
That's it!