Question

super confused with these things please help:

(x+2)/1 - (x^2+x-6)/x-3


HOW?! The answer is -2x/(x-3)

Answer 1

[(x+2)(x-3) - (x^2+x-6)]/(x-3)
= [x^2-x-6-x^2-x+6]/(x-3)
= -2x/(x-3)

Answer 2

\[\frac{x+2}{1} - \frac{x^2 + x -6}{x-3}\]
Multiply the first fraction by \(x-3\) to get common denominators.
\[\frac{x-3}{x-3} \times \frac{x+2}{1} - \frac{x^2 + x -6}{x-3}\]
\[\frac{x^2 -x-6}{x-3} - \frac{x^2 + x -6}{x-3}\]
Now subtract your numerators:
\(x^2-x^2 = 0 \rightarrow -x -x = 2x \rightarrow -6 +6 = 0\) Leaving you with:
\[\frac{2x} {x-3}\]

Answer 3

(@Srini143 - factoring doesn't help much here to get rid of denominators)

Answer 4

(it doesn't help at all)

Answer 5

(x^2+x-6) factors to (x-1)(x+3)

Answer 6

Correction -x -x = -2x and the resulting equation is
\[\frac{-2x} {x-3}\]
Sorry.