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

1 Answer
May 25, 2018

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

Explanation:

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)