Question

What is the quotient?

Answer 1

`\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)\\\\(t+3)/(t+4)/(t^2+7t+12)=(t+3)/(t+4)/[(t+4)(t+3)]\\\\=(t+3)/(t+4)\cdot(1)/((t+4)(t+3))\\\\\text{canceled}\ t+3\\\\=(1)/(t+4)\cdot(1)/(t+4)=\boxed{(1)/((t+4)^2)}`