Question 97207
{{{4/(a^2 - 1)  +  1/(2a + 2)}}} Start with the given expression



{{{4/(a+1)(a-1)  +  1/(2a + 2)}}} Factor {{{a^2-1}}} to {{{(a+1)(a-1)}}}



{{{4/(a+1)(a-1)  +  1/2(a + 1)}}} Factor {{{2a+2}}} to {{{2(a+1)}}}



So our LCD is {{{2(a+1)(a-1)}}} (this is what we want the denominators to get to)



{{{(2/2)(4/(a+1)(a-1))  +  1/2(a + 1)}}} Multiply the first fraction by {{{2/2}}}


{{{(2/2)(4/(a+1)(a-1))  +  ((a-1)/(a-1))(1/2(a + 1))}}} Multiply the second fraction by {{{(a-1)/(a-1)}}}



{{{(8/2(a+1)(a-1))  +  ((a-1)/2(a + 1)(a-1))}}} Multiply



{{{(8+a-1)/2(a + 1)(a-1)}}} Combine the fractions. We can do this since the denominators are the same.


{{{(7+a)/2(a + 1)(a-1)}}} Combine like terms