Question

Add and simplify. What is the restriction on x?


`x\\eq _________`

`(2)/(x+4) +(x)/(x-3)`

Answer 1

`\cfrac{2}{x+4}~~ + ~~\cfrac{x}{x-3}\implies \cfrac{(x-3)2~~ + ~~(x+4)x}{\underset{\textit{using this LCD}}{(x+4)(x-3)}} \\\\\\ \cfrac{2x-6+x^2+4x}{(x+4)(x-3)} \implies \cfrac{x^2+6x-6}{(x+4)(x-3)}\qquad x\\e -4,3`

why can't it be -4 or 3? for if it ever does become -4 or 3, the denominator will turn to 0, giving an undefined fraction.