Question 328226
<pre><b>
{{{7/(x-4)}}}{{{""+""}}}{{{4/(x+4)}}}{{{""=""}}}{{{(-5x)/(x^2-16)}}}

Factor the denominator on the right:

{{{7/(x-4)}}}{{{""+""}}}{{{4/(x+4)}}}{{{""=""}}}{{{(-5x)/((x-4)(x+4))}}}

Multiply every term through by the LCD which is (x-4)(x+4), written as {{{red((x-4)(x+4)/1)}}}


{{{7/(x-4)}}}{{{red(""*"")}}}{{{red((x-4)(x+4)/1)}}}{{{""+""}}}{{{4/(x+4)}}}{{{red(""*"")}}}{{{red((x-4)(x+4)/1)}}}{{{""=""}}}{{{(-5x)/((x-4)(x+4))}}}{{{red(""*"")}}}{{{red((x-4)(x+4)/1)}}}

Cancel what will cancel:

{{{7/(cross(x-4))}}}{{{red(""*"")}}}{{{red((cross(x-4))(x+4)/1)}}}{{{""+""}}}{{{4/(cross(x+4))}}}{{{red(""*"")}}}{{{red((x-4)(cross(x+4))/1)}}}{{{""=""}}}{{{(-5x)/((cross(x-4))(cross(x+4)))}}}{{{red(""*"")}}}{{{red((cross(x-4))(cross(x+4))/1)}}}

{{{7}}}{{{red(""*"")}}}{{{red((x+4))}}}{{{""+""}}}{{{4}}}{{{red(""*"")}}}{{{red((x-4))}}}{{{""=""}}}{{{-5x}}}

{{{7x+28}}}{{{""+""}}}{{{4x-16}}}{{{""=""}}}{{{-5x}}}

{{{11x+12}}}{{{""=""}}}{{{-5x}}}

{{{16x}}}{{{""=""}}}{{{-12}}}

{{{x}}}{{{""=""}}}{{{-12/16}}}

{{{x}}}{{{""=""}}}{{{-3/4}}}

Edwin</pre>