Question 1058747

Can you please help me simplify this:

(cosx)/(1-tanx) + (sinx*cosx)/(sinx-cosx)
<pre>{{{cos (x)/(1 - tan (x)) + (sin (x) * cos (x))/(sin (x) - cos (x))}}}
{{{cos (x)/(1 - sin (x)/cos (x)) + (sin (x) * cos (x))/(sin (x) - cos (x))}}} ------ Substituting {{{matrix(1,3, sin (x)/cos (x), for, tan (x))}}}
{{{cos (x)/((cos (x) - sin (x))/cos (x)) + (sin (x) * cos (x))/(sin (x) - cos (x))}}} <b>======></b> {{{matrix(1,3, cos (x)/1, "÷", ((cos (x) - sin (x))/cos (x)) + (sin (x) * cos (x))/(sin (x) - cos (x)))}}} 
{{{matrix(1,3, cos (x)/1, "*", cos (x)/(cos (x) - sin (x)) + (sin (x) * cos (x))/(sin (x) - cos (x)))}}} ----- Applying KCF (KEEP, CHANGE, FLIP) to LEFT of "+"
{{{cos^2 (x)/(cos (x) - sin (x)) + (sin (x) * cos (x))/(sin (x) - cos (x)))}}} 
{{{(- cos^2 (x) + sin (x) * cos (x))/(- (cos (x) - sin (x)))}}} ------- Multiplying by LCD, - (cos x - sin x)
{{{(cos (x) * (- 1) * (cos (x) - sin (x)))/(- (cos (x) - sin (x)))}}} <b>======></b> {{{(cos (x) * cross((- 1) * (cos (x) - sin (x))))/cross((- (cos (x) - sin (x))))}}} <b>======></b> {{{highlight(highlight_green(highlight(cos (x))))}}}