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

2 Answers
Sahar Mulla ❤
Apr 4, 2018

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

#=>x^2[1/(x-2)^2 +1/(x+2)^2]#

#=>x^2[((x+2)^2 +(x-2)^2)/((x-2)^2(x+2)^2)]#

#=>x^2[(x^2 + 4 + 4x + x^2 + 4 - 4x)/(((x-2)(x+2))^2)]#

#=>x^2[(2x^2 + 8)/(x^2-4)^2]#

#=>2x^2[(x^2 + 4)/(x^2-4)^2]#

Noah G
Apr 4, 2018

We start by expanding:

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

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

#(x^4 + 4x^3 + 4x^2 + x^4 - 4x^3 + 4x^2)/((x + 2)^2(x - 2)^2)#

#(2x^4 + 8x^2)/((x +2)^2(x - 2)^2#

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

Hopefully this helps!

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