Question

Simplify and select the answer with the appropriate restrictions for the variables. 4x^2 + 8x/x^2 - x - 6

Answer 1

`(4x^2+8x)/(x^2-x-6)\\\\Domain:x^2-x-6\\eq0\\\\x^2-3x+2x-3\cdot2=x(x-3)+2(x-3)=(x-3)(x+2)\\\\x^2-x-6\\eq0\iff(x-3)(x+2)\\eq0\iff x-3\\eq0\ or\ x+2\\eq0\\\\therefore\ x\\eq3\ and\ x\\eq-2\\------------------\\the\ nominator:\ 4x^2+8x=4x\cdot x+4x\cdot2=4x(x+2)\\the\ denominator:x^2-x-6=(x-3)(x+2)`


`therefore\ simplify\ form:\\\\(4x^2+8x)/(x^2-x-6)=(4x(x+2))/((x-3)(x+2))=\boxed{(4x)/(x-3)}`