Question 175243
simplify each sum:
{{{(-3x)/(x^2-9)}}} + {{{(4)/(2x-6)}}}
The 1st denominator is the "difference of squares"; the 2nd denominator can also be factored;
{{{(-3x)/((x-3)(x+3))}}} + {{{(4)/(2(x-3))}}}
The common denominator will be 2(x+3)(x-3)so we have
{{{(2(-3x) + 4(x+3))/(2(x+3)(x-3))}}} = {{{(-6x + 4x + 12)/(2(x+3)(x-3))}}} = {{{(-2x + 12)/(2(x+3)(x-3))}}}
Factor out 2 in the numerator, then cancel the twos
{{{2(-x + 6)/(2(x+3)(x-3))}}} = {{{(-x + 6)/((x+3)(x-3))}}}
 
and
these instructions say simplify each complex fraction:
(-3)/(5/x+y)
:
When dividing fractions invert the dividing fraction and multiply
-3 * {{{((x+y))/5}}} = {{{-(3(x+y))/5}}}