Question 132126
Solve for x:
I'm assuming that you have a typo in the term:{{{4/(a-4)}}} and that it should read:{{{4/(x-4)}}}, so, proceeding on that assumption:
{{{(x/(x+4))-(4/(x-4)) = (x^2+16)/(x^2-16)}}} Simplify the fractions on the left side by finding the common denominator of (x+4)(x-4):
{{{(x(x-4)-4(x+4))/((x+4)(x-4)) = (x^2+16)/(x^2-16)}}} On the left side, simplify the numerator and perform the indicated multiplication in the denominator.
{{{(x^2-4x-4x-16)/(x^2-16) = (x^2+16)/(x^2-16)}}} Applying the rule: If{{{a/b = c/b}}} then {{{a = c}}}
{{{x^2-8x-16 = x^2+16}}} Subtract {{{x^2}}} from both sides.
{{{-8x-16 = 16}}} Add 16 to both sides.
{{{-8x = 32}}} Divide both sides by -8
{{{x = -4}}} which is choice B, however, when you substitute x = -4 into the original equation, you get:
{{{((-4)/(-4+4))-(4/(-4-4)) = ((-4)^2+16)/((-4)^2-16)}}} Simplifying:
{{{((-4)/0)-(4/(-8)) = (32/0)}}}...and, as you know, division by zero is not defined and thefore, not permitted.
So the solution would have to be NO SOLUTION or choice C.