Answer
$(x+3)$ and $(x-2)$.
$(x+3)$ and $(x+1)$.
$(x+3)(x-2)(x+1)$.
Work Step by Step
The given expression is
$\frac{x-1}{x^2+x-6}-\frac{x-2}{x^2+4x+3}$
The first denominator is $x^2+x-6$.
Rewrite the middle term $x$ as $3x-2x$.
$x^2+3x-2x-6$
Group terms.
$(x^2+3x)+(-2x-6)$
Factor each term.
$x(x+3)-2(x+3)$
Factor out $(x+3)$.
$(x+3)(x-2)$
The factor of the first denominator is $(x+3)(x-2)$.
The second denominator is $x^2+4x+3$.
Rewrite the middle term $4x$ as $3x+x$.
$x^2+3x+x+3$
Group terms.
$(x^2+3x)+(x+3)$
Factor each term.
$x(x+3)+1(x+3)$
Factor out $(x+3)$.
$(x+3)(x+1)$
The factor of the second denominator is $(x+3)(x+1)$.
The LCD of both denominators is $(x+3)(x-2)(x+1)$.
