Simplify #(x-2)/(x^2+6x+9)-(x+2)/(2x^2-18)#?

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Answer 1 · 2018-05-25T10:42:33

#(x^2-15x+6)/(2(x-3)(x+3)^2)#

#x^2+6x+9=(x+3)(x+3)=(x+3)^2#

#2x^2-18=2(x^2-9)=2(x-3)(x+3)#
Difference of 2 squares #(a-b)(a+b)=a^2-b^2#

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

Multiply by #2(x-3)(x+3)^2#

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

Expand the brackets

= #(2(x^2-5x+6)-(x^2+5x+6))/(2(x-3)(x+3)^2)#

Further expand the brackets

= #(2x^2-10x+12-x^2-5x-6)/(2(x-3)(x+3)^2)#

Simplify

= #(x^2-15x+6)/(2(x-3)(x+3)^2)#