How do you solve #x/(x+2) - 2/(x-2) = (x^2+4)/(x^2-4)#?

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Answer 1 · 2016-02-16T15:37:27

You must make all the fractions equivalent by putting them on an equivalent denominator.

The LCD (Least Common Denominator) is (x + 2)(x - 2).

#(x(x - 2))/((x + 2)(x - 2)) - (2(x + 2))/((x - 2)(x + 2)) = (x^2 + 4)/((x - 2)(x + 2))#

We can now eliminate the denominators.

#x^2 - 2x - 2x - 4 = x^2 + 4#

#x^2 - x^2 - 4x - 8 = 0#

#-4x = 8#

#x = -2#

Since x= -2 makes some of the denominators equal to 0, there is no solution to the equation.

Hooefully this helps!