A fraction is a way to describe a part of a whole. The quotient of the fraction is 1/(t+4)².
A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The quotient of [tex]\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}[/tex] can be found by factorizing the denominator of the fraction. Therefore, the factors of the denominator are,
t² + 7t + 12
= t² + 4t + 3t + 12
= t(t+4) +3(t+4)
= (t+4)(t+3)
Now, quotient will be,
[tex]\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}\\\\\\=\dfrac{\dfrac{t+3}{t+4}}{(t+4)(t+3)}\\\\\\=\dfrac{(t+3)}{(t+4)(t+3)(t+4)}\\\\\\= \dfrac1{(t+4)^2}[/tex]
Hence, the quotient of the fraction is 1/(t+4)².
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