Question 193641
Solve for a:
{{{3-((a-5)/(a+5)) = (a^2-15)/(a+5)}}} Simplify the left side.
{{{(3(a+5)-(a-5))/(a+5) = (a^2-15)/(a+5)}}}
{{{(3a+15-a+5)/(a+5) = (a^2-15)/(a+5)}}}
{{{(2a+20)/(a+5) = (a^2-15)/(a+5)}}} Multiply both sides by (a+5).
{{{2a+20 = a^2-15}}} Rearrange this to form a quadratic equation in standard form.
{{{a^2-2a-35 = 0}}} Factor.
{{{(a-7)(a+5) = 0}}}
{{{a = 7}}} or {{{a = -5}}} But...if we substitute a = -5 into the original equation then we have division by zero which, of course, is a no-no! So a = -5 is and excluded solution.
The acceptable solution is:
{{{highlight(a = 7)}}}