Question 630792
can you help me please by subtracting this rational expression
{{{(x)/(x^2 - 5x + 6)}}} - {{{(3)/(3-x)}}}
;
Factor the 1st denominator
{{{(x)/((x-2)(x-3))}}} - {{{(3)/(3-x)}}}
;
Convert the 2nd denominator, factor out -1
{{{(x)/((x-2)(x-3))}}} - {{{(3)/(-1(x-3))}}}
:
the minus one changes the sign
{{{(x)/((x-2)(x-3))}}} + {{{(3)/((x-3))}}}
;
The common denominator is (x-2)(x-3)
{{{(x + 3(x-2))/((x-2)(x-3))}}} = {{{(x+3x-6)/((x-2)(x-3))}}} = {{{(4x-6)/((x-2)(x-3))}}}
Or you can Factor out 2
{{{(2(2x-3))/((x-2)(x-3))}}}
:
Did all this make sense to you?