I keep having problem with simplification problems...

My problem is: $\displaystyle \frac{6tan(x)}{1+sec(x)}+\frac{6+6sec(x)}{tan(x)}$

The answer given is: $\displaystyle 12csc(x)$ but I cannot reach this answer.

My attempt is...

$\displaystyle \frac{6tan^2(x)}{tan(x)[1+sec(x)]}+\frac{[1+sec(x)](6+6sec(x))}{tan(x)[1+sec(x)]}$ =

$\displaystyle \frac{6tan^2(x)}{tan(x)[1+sec(x)]}+\frac{6+12sec(x)+6sec^2(x)}{tan(x)[1+sec(x)]}$ =

$\displaystyle \frac{6tan^2(x) +6sec^2(x) + 12sec(x)+ 6}{tan(x)[1+sec(x)]}$ =

$\displaystyle \frac{6(tan^2(x) +sec^2(x) + 2sec(x)+ 1)}{tan(x)[1+sec(x)]}$ =

$\displaystyle \frac{6(tan^2(x) +sec^2(x) + 2sec(x)+ 1)}{tan(x)[1+sec(x)]}$ =

$\displaystyle \frac{6(2sec^2(x) + 2sec(x))}{tan(x)[1+sec(x)]}$