Respuesta :
The simplification of difference of the given two rational expressions [tex]\frac{1}{x^{2} -4}+\frac{6}{x+2}[/tex] is equal to (6x-11)/ (x-2)(x+2).Restriction on the variables is given by x≠ -2, x≠ 2.
As given in the question,
Given expression is [tex]\frac{1}{x^{2} -4}+\frac{6}{x+2}[/tex]
Simplify the given two rational expressions by factorizing them,
[tex]\frac{1}{x^{2} -4}+\frac{6}{x+2}\\\\= \frac{1}{(x-2)(x+2)}+\frac{6}{x+2}\\\\= \frac{1+6(x-2)}{(x-2)(x+2)}\\\\= \frac{1+6x-12}{(x-2)(x+2)}\\\\= \frac{(6x-11)}{(x-2)(x+2)}[/tex]
Restriction on the variables is given by x≠ -2, x≠2.
Therefore, the simplification of difference of the given two rational expressions [tex]\frac{1}{x^{2} -4}+\frac{6}{x+2}[/tex] is equal to (6x-11)/ (x-2)(x+2). Restriction on the variables is given by x≠ -2, x≠ 2.
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