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  • 21-01-2019
  • Mathematics
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What is the quotient?

What is the quotient class=

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  • 21-01-2019

[tex]\text{First factor}\ t^2+7t+12=t^2+4t+3t+12=t(t+4)+3(t+4)\\\\=t^2+7t+12=(t+4)(t+3)\\\\\dfrac{t+3}{t+4}\div(t^2+7t+12)=\dfrac{t+3}{t+4}\div[(t+4)(t+3)]\\\\=\dfrac{t+3}{t+4}\cdot\dfrac{1}{(t+4)(t+3)}\\\\\text{canceled}\ t+3\\\\=\dfrac{1}{t+4}\cdot\dfrac{1}{t+4}=\boxed{\dfrac{1}{(t+4)^2}}[/tex]

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