Question 143103
Simplify:{{{ (7x - 9) /  (x^2 - 25) }}} - {{{ 3 / (x - 5) }}} = {{{ 2 / (x - 5) }}}

First, we need to recognize that {{{(x^2-25)}}}={{{(x-5)(x+5)}}}
So, {{{x^2-25}}} is the LCM and we need to multiply each term by {{{x^2-25)}}}.  When we do, we get:

{{{(7x-9)-3(x+5)=2(x+5)}}}  get rid of parens
{{{7x-9-3x-15=2x+10}}} or
{{{4x-24=2x+10}}} add 24 to and subtract 2x from each side:

{{{4x-24+24-2x=2x-2x+24+10}}} collect like terms

{{{2x=34}}}  divide each side by 2
{{{x=17}}}----------------------------------ans


Hope this helps---ptaylor