Question

If x>2,then x2-x-6/x2-4=

Answer 1

`(x^2-x-6)/(x^2-4)=(*)\\------------\\x^2-x-6=0\\a=1;\ b=-1;\ c=-6\\\Delta=b^2-4ac;\ \Delta=(-1)^2-4\cdot1\cdot(-6)=1+24=25\\\\x_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\\\\x_1=(1-√(25))/(2\cdot1)=(1-5)/(2)=(-4)/(2)=-2\\\\x_2=(1+√(25))/(2\cdot1)=(1+5)/(2)=(6)/(2)=3\\\\x^2-x-6=(x+2)(x-3)`

`---------------------\\x^2-4=x^2-2^2=(x-2)(x+2)\\-------------------\\\\(*)=((x+2)(x-3))/((x-2)(x+2))=(x-3)/(x-2)`