How do you subtract and simplify #\frac { x } { x + 2} - \frac { 2} { x ^ { 2} - 4}#?

1 Answer
smendyka
Mar 8, 2017

See the entire solution process below:

Explanation:

First, in order to add or subtract fractions they must be over a common denominator.

#x^2 - 4# factored gives: #(x + 2)(x - 2)#

Therefore, to put both fractions over a common denominator we must multiply the fraction on the left by the appropriate form of #1# or #(x - 2)/(x -2)#:

#((x - 2)/(x - 2) xx x/(x + 2)) - 2/(x^2 - 4) ->#

#(x(x - 2))/(x^2 - 4) - 2/(x^2 - 4) ->#

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

Now, with each fraction over a common denominator we can subtract the numerators:

#((x^2 - 2x) - 2)/(x^2 - 4) -> (x^2 - 2x - 2)/(x^2 - 4)#

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