Question 425367
Solve for a:
{{{4a-3 = (a+13)/(a+1)}}} Multiply both sides by {{{(a+1)}}}
{{{(4a-3)(a+1) = (a+13)cross((a+1))/cross((a+1))}}} Cancel as indicated.
{{{(4a-3)(a+1) = (a+13)}}} Simplify.
{{{4a^2+a-3 = a+13}}} Subtract {{{a+13}}} from both sides.
{{{4a^2-16 = 0}}} Factor this difference of two squares.
{{{(2a+4)(2a-4) = 0}}} Apply the zero product rule.
{{{2a+4 = 0}}} or {{{2a-4 = 0}}} so...
{{{2a = -4}}} then {{{a[1] = -2}}} or {{{2a = 4}}} then {{{a[2] = 2}}}
The answer:
{{{a[1] = -2}}}, {{{a[2] = 2}}}