Question 72678
Solve for x:
{{{ax+b(ax-b) = a(bx-a)-bx}}} Expand the parentheses.
{{{ax+abx-b^2 = abx-a^2-bx}}} Simplify. Subtract abx from both sides.
{{{ax-b^2 = -a^2-bx}}} Add {{{a^2}}} to both sides.
{{{a^2-b^2+ax = -bx}}} Add bx to both sides.
{{{a^2-b^2+ax+bx = 0}}} Simplify.
{{{(a^2-b^2)+x(a+b) = 0}}} Subtract {{{(a^2-b^2)}}} from both sides.
{{{x(a+b) = -(a^2-b^2)}}} Divide both sides by {{{(a+b)}}}
{{{x = -(a^2-b^2)/(a+b)}}} Factor the numerator.
{{{x = -((a+b)(a-b))/(a+b)}}} Cancel the{{{(a+b)}}}
{{{x = -(a-b)}}}
{{{x = b-a}}}