SOLUTION: seven divided by the difference of a number and 2 minus 6 divided by a number plus 2 equals 6 times the reciprocal of the difference of the number squared and 4, whats the number?

Question 443818: seven divided by the difference of a number and 2 minus 6 divided by a number plus 2 equals 6 times the reciprocal of the difference of the number squared and 4, whats the number?
Answer by karaoz(32) (Show Source): You can put this solution on YOUR website!

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/(x²-4). What is x?

Note that the denominators in three fractions are (x-2), (x+2) and (x²-4). Also, note that (x²-4) = (x-2)*(x+2).

After multiplying both sides of the equation by (x²-4), we have:
7(x²-4)/(x-2) - 6(x²-4)/(x+2) = 6(x²-4)/(x²-4), 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

After expanding the brackets:
7x + 14 - 6x + 12 = 6

After simplifying the left hand side:
x + 26 = 6

After taking away 26 from both sides of the equation:
x = -20.

That's it!
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