Simplify $\frac{x - 2}{x^{2} + 6 x + 9} - \frac{x + 2}{2 x^{2} - 18}$ $(x-2)/(x^2+6x+9)-(x+2)/(2x^2-18)$ ?

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Simplify $\frac{x - 2}{x^{2} + 6 x + 9} - \frac{x + 2}{2 x^{2} - 18}$ $(x-2)/(x^2+6x+9)-(x+2)/(2x^2-18)$ ?

1 Answer

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Answer 1 · 2018-05-25T10:42:33

$\frac{x^{2} - 15 x + 6}{2 (x - 3) {(x + 3)}^{2}}$ $(x^2-15x+6)/(2(x-3)(x+3)^2)$

Explanation:

$x^{2} + 6 x + 9 = (x + 3) (x + 3) = {(x + 3)}^{2}$ $x^2+6x+9=(x+3)(x+3)=(x+3)^2$

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

$\frac{x - 2}{{(x + 3)}^{2}} - \frac{x + 2}{2 (x - 3) (x + 3)}$ $(x-2)/(x+3)^2-(x+2)/(2(x-3)(x+3))$

Multiply by $2 (x - 3) {(x + 3)}^{2}$ $2(x-3)(x+3)^2$

= $\frac{(x - 2) (2) (x - 3) - (x + 2) (x + 3)}{2 (x - 3) {(x + 3)}^{2}}$ $((x-2)(2)(x-3)-(x+2)(x+3))/(2(x-3)(x+3)^2)$

Expand the brackets

= $\frac{2 (x^{2} - 5 x + 6) - (x^{2} + 5 x + 6)}{2 (x - 3) {(x + 3)}^{2}}$ $(2(x^2-5x+6)-(x^2+5x+6))/(2(x-3)(x+3)^2)$

Further expand the brackets

= $\frac{2 x^{2} - 10 x + 12 - x^{2} - 5 x - 6}{2 (x - 3) {(x + 3)}^{2}}$ $(2x^2-10x+12-x^2-5x-6)/(2(x-3)(x+3)^2)$

Simplify

= $\frac{x^{2} - 15 x + 6}{2 (x - 3) {(x + 3)}^{2}}$ $(x^2-15x+6)/(2(x-3)(x+3)^2)$

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Simplify $\frac{x - 2}{x^{2} + 6 x + 9} - \frac{x + 2}{2 x^{2} - 18}$ $(x-2)/(x^2+6x+9)-(x+2)/(2x^2-18)$ ?

1 Answer

Explanation:

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Simplify x−2x2+6x+9−x+22x2−18(x-2)/(x^2+6x+9)-(x+2)/(2x^2-18)?

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Explanation:

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Simplify $\frac{x - 2}{x^{2} + 6 x + 9} - \frac{x + 2}{2 x^{2} - 18}$ $(x-2)/(x^2+6x+9)-(x+2)/(2x^2-18)$ ?