Thread: check this please

can someone tell me if this is right
simplify

3x
x

minus

x
x+1

my answer is
2x^2+4x
x(x+1)

$\displaystyle
\frac{3x}{x}-\frac{x}{x+1}=
$
multiplying by $\displaystyle (x+1)$ for the left fraction and $\displaystyle (x)$ for the right fraction gives

$\displaystyle
\frac{3x(x+1)-x*(x)}{x(x+1)}=
$
simplifying the numerator

$\displaystyle \frac{3x^2+3x-x^2}{x(x+1)}=$

more simplifying

$\displaystyle \frac{2x^2+3x}{x(x+1)}=$

factoring $\displaystyle x$ out of the numerator and canceling it with the $\displaystyle x$ in the denominator leaves

$\displaystyle
\frac{2x+3}{x+1}
$