Question

What is the quotient? StartFraction t 3 Over t 4 EndFraction divided by (t squared 7 t 12) (t 3) squared (t 4) squared StartFraction 1 Over (t 4) squared EndFraction StartFraction 1 Over (t 3) squared EndFraction.

Answer 1

The simplified form of the expression is $\frac{1}{(t+4)^2}$

Given the expression:

• $\dfrac{\frac{t+3}{t+4} }{t^2+7t+12}$

Factorize the denominator as shown:

t^2 + 7t + 12

t^2 + 4t + 3t + 12

t(t+4) + 3(t+4)

(t+4)(t+3)

Substituting into the expression above, we will have:

$= \dfrac{\frac{t+3}{t+4} }{(t+3)(t+4)}\\=\dfrac{t+3}{t+4} \div (t+3)(t+4)\\=\dfrac{t+3}{t+4} \times \dfrac{1}{(t+3)(t+4)} \\=\dfrac{1}{(t+4)^2}$

Hence the simplified form of the expression is $\frac{1}{(t+4)^2}$

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