document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #325619 by karaoz(32) $\"\"$ $\"About$

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\n" ); document.write( "This is a funny question. I wonder what is the purpose of it.
\n" ); document.write( "Let this jumpy number be called x!
\n" ); document.write( "Then translating the problem statement using algebraic symbols for operators and x for \"a number\" we have the following:
\n" ); document.write( "7/(x-2) - 6/(x+2) = 6*1/(x²-4). What is x?

\n" ); document.write( "Note that the denominators in three fractions are (x-2), (x+2) and (x²-4). Also, note that (x²-4) = (x-2)*(x+2).

\n" ); document.write( "After multiplying both sides of the equation by (x²-4), we have:
\n" ); document.write( "7(x²-4)/(x-2) - 6(x²-4)/(x+2) = 6(x²-4)/(x²-4), which becomes:
\n" ); document.write( "7(x-2)(x+2)/(x-2) - 6(x-2)(x+2)/(x+2) = 6, which is the same as
\n" ); document.write( "7(x+2) - 6(x-2) = 6

\n" ); document.write( "After expanding the brackets:
\n" ); document.write( "7x + 14 - 6x + 12 = 6

\n" ); document.write( "After simplifying the left hand side:
\n" ); document.write( "x + 26 = 6

\n" ); document.write( "After taking away 26 from both sides of the equation:
\n" ); document.write( "x = -20.

\n" ); document.write( "That's it! \n" ); document.write( "

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