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harkovskaia [24]
3 years ago
15

What is the quotient?

Mathematics
1 answer:
pshichka [43]3 years ago
7 0

\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}}

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Step by step solution :

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Equation at the end of step  1  :

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Step  2  :

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Equation at the end of step  2  :

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Step  3  :

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Step-by-step explanation:

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