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# Show that 3 - 2x^2 + 11x + 12 / x^2 +7x +12 can be simplified to x+6 / x+3

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Show that 3 - 2x^2 + 11x + 12 / x^2 +7x +12 can be simplified to x+6 / x+3

thx

YEEEEEET  Nov 11, 2017

#3
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\(3-\dfrac{2x^2+11x+12}{x^2+7x+12}\\ =3-\dfrac{(2x+3)(x+4)}{(x+3)(x+4)}\\ =3-\dfrac{2x+3}{x+3}\;,\;x\neq-4\\ =\dfrac{3x+9}{x+3}-\dfrac{2x+3}{x+3}\;,\;x\neq-4\\ =\dfrac{x+6}{x+3}\;,\;x\neq-4\)

MaxWong  Nov 12, 2017
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#1
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Check your question and make sure it is OK. "3 -" at the beginning??

Guest Nov 12, 2017
#2
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ye its definitely 3- which is why im confused

YEEEEEET  Nov 12, 2017
edited by YEEEEEET  Nov 12, 2017
#3
+6925
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\(3-\dfrac{2x^2+11x+12}{x^2+7x+12}\\ =3-\dfrac{(2x+3)(x+4)}{(x+3)(x+4)}\\ =3-\dfrac{2x+3}{x+3}\;,\;x\neq-4\\ =\dfrac{3x+9}{x+3}-\dfrac{2x+3}{x+3}\;,\;x\neq-4\\ =\dfrac{x+6}{x+3}\;,\;x\neq-4\)

MaxWong  Nov 12, 2017
#4
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i have no idea how you simplified the 3- can you explain that please thx

YEEEEEET  Nov 12, 2017
#5
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Max used the common denominator x + 3 as follows:

3/1 - [2x + 3 /x + 3]   Use the common denominator of x + 3 and multiply it by 3:

3[x + 3] - [2x + 3] /[x + 3]

[3x + 9]   [2x + 3]

_____  _  _____

[x + 3]       [x + 3]

Guest Nov 12, 2017

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