Question

Solve f(x)=x²+7x+12/-x²-3x+4

Answer 1

`x^2+7x+12=x^2+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)\\\\-x^2-3x+4=-(x^2+3x-4)=-(x^2+4x-x-4)\\\\=-[x(x+4)-1(x+4)]=-(x+4)(x-1)\\\\f(x)=(x^2+7x+12)/(-x^2-3x+4)=((x+4)(x+3))/(-(x+4)(x-1))\\\\\text{The domain:} x\\eq-4\ and\ x\\eq1\\\\canceled\ (x+4)\\\\f(x)=(x+3)/(-(x-1))=-(x+3)/(x-1)\ for\ x\\eq-4\ and\ x=1`