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

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

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