Respuestas

2012-04-27T21:51:32+02:00

1.-

 

\frac{2}{X+4}+\frac{1}{X-3}=\frac{2(X-3)+X+4}{(X-3)(X+4)} =\frac{2X-6+X+4}{(X-3)(X+4)}=\frac{3X-2}{(X-3)(X+4)}

 

2.-

\frac{x}{x-y}+\frac{x}{x+y}=\frac{x(x+y)+x(x-y)}{(x-y)(x+y)}=\frac{x^{2}+xy+x^{2}-xy}{(x-y)(x+y)}=\frac{x^{2}+x^{2}}{x^{2}-y^{2}}=\frac{2x^{2}}{x^{2}-y^{2}}

 

3.-

\frac{x+y}{x-y}+\frac{x-y}{x+y}=\frac{(x+y)^{2}+(x-y)^{2}}{x^{2}-y^{2}}= \frac{x^{2}+2xy+y^{2}+x^{2}-2xy+y^{2}}{x^{2}-y^{2}}=

==\frac{2x^{2}+2y^{2}}{x^{2}-y^{2}}=\frac{2(x^{2}+y^{2})}{x^{2}-y^{2}}

 

4.-

\frac{3}{x-5}+\frac{3x}{x^{2}-25}=\frac{3(x+5)+3x}{(x-5)(x+5)}=\frac{3x+15+3x}{(x-5)(x+5)}=\frac{6x+15}{(x-5)(x+5)}

 

5.-

\frac{x+4}{x-3a}+\frac{3a^{2}-x^{2}}{x^{2}-9a^{2}}=\frac{(x+4)(x+3a)+3a^{2}-x^{2}}{(x-3a)(x+3a)}= \frac{3ax+4x+12a+3a^{2}}{x^{2}-9a^{2}}

 

 

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