Express as a single fraction in its simplest form. `(x+3)/((x+1)(x+2))-(x+1)/(x^2+5x+6)` Thanks ``

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llltkl | College Teacher | (Level 3) Valedictorian

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To simplify:`(x+3)/((x+1)(x+2))-(x+1)/(x^2+5x+6)`

`=(x+3)/((x+1)(x+2))-(x+1)/(x^2+3x+2x+6)`

`=(x+3)/((x+1)(x+2))-(x+1)/(x(x+3)+2(x+3))`

`=(x+3)/((x+1)(x+2))-(x+1)/((x+3)(x+2))`

`=((x+3)^2-(x+1)^2)/((x+1)(x+2)(x+3))`

`=((x+3+x+1)(x+3-x-1))/((x+1)(x+2)(x+3))`

`=(2(2x+4))/((x+1)(x+2)(x+3))`

`=(4(x+2))/((x+1)(x+2)(x+3))`

`=4/((x+1)(x+3))` `rarr` answer.

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