Question 271684
{{{(a-1)/red(a+1) + (a+1)/green(a-1)}}} I need to add the fractions together! 
<pre><font size = 4 color = "indigo"><b>
Put parentheses around all the numerators and denominators:

{{{((a-1))/red((a+1)) + ((a+1))/green((a-1))}}}

The LCD is {{{red((a+1))green((a-1))}}}

The first fraction's denominator needs an {{{green((a-1))}}} to become
the LCD, so we multiply it by {{{green((a-1))/green((a-1))}}} which 
equals 1 and thus will not change the value.


{{{((a-1)green((a-1)))/(red((a+1))green((a-1))) + ((a+1))/green((a-1))}}}

The second fraction's denominator needs an {{{red((a+1))}}} to become
the LCD, so we multiply it by {{{red((a+1))/red((a+1))}}} which 
equals 1 and thus will not change the value.


{{{((a-1)green((a-1)))/(red((a+1))green((a-1))) + 

((a+1)red((a+1)))/(green((a-1))red((a+1)))}}}

Now the denominators are the same in value so we can
combinew the numerators over the LCD:

{{{((a-1)green((a-1)) + 

(a+1)red((a+1)))/(green((a-1))red((a+1)))}}}

Multiply the numerator out but not the denominator.


{{{((a^2-2a+1) + 

(a^2+2a+1))/((a-1)(a+1))}}}

{{{(a^2-2a+1 + 

a^2+2a+1)/((a-1)(a+1))}}}

{{{(a^2-cross(2a)+1 + 

a^2+cross(2a)+1)/((a-1)(a+1))}}}

{{{(2a^2 +2)/((a-1)(a+1))}}}

{{{(2(a^2 +1))/((a-1)(a+1))}}}

Since nothing will factor or cancel further,
we may multiply the numerator and demominate back out:

{{{(2a^2 +2)/(a^2-1)}}}

Edwin</pre>