Question 81902
10.  Solve for x:
{{{x/(x^2-3) = 5/(x+4)}}} Multiply both sides by{{{(x^2-3)(x+4)}}}
{{{x*cross((x^2-3))(x+4)/cross((x^2-3)) = 5(x^2-3)cross((x+4))/cross((x+4))}}} Cancel as indicated and simplify.
{{{x(x+4) = 5(x^2-3)}}}
{{{x^2+4x = 5x^2-15}}} Subtract x^2 from both sides.
{{{4x = 4x^2-15}}} Subtract 4x from both sides.
{{{4x^2-4x-15 = 0}}} Factor this quadratic equation.
{{{(2x+3)(2x-5) = 0}}} Apply the zero products principle.
{{{2x+3 = 0}}} and/or {{{2x-5 = 0}}}
{{{2x = -3}}} so {{{x = -3/2}}}
{{{2x = 5}}} so {{{x = 5/2}}}
Solutions:
{{{x = -3/2}}}
{{{x = 5/2}}}

14. Solve for w:
{{{4w/(3w-2) + 2w/(3w+2) = 2}}} Multiply both sides by{{{(3w-2)(3w+2)}}}
{{{4w*cross((3w-2))(3w+2)/cross((3w-2)) + 2w(3w-2)cross((3w+2))/cross((3w+2)) = 2(3w-2)(3w+2)}}} Simplify.
{{{4w(3w+2) + 2w(3w-2) = 2(9w^2-4)}}}
{{{(12w^2+8w) + (6w^2-4w) = 18w^2-8}}}
{{{(18w^2)+4w = (18w^2)-8}}} Subtract{{{18w^2}}} from both sides.
{{{4w = -8}}} Divide both sides by 4.
{{{w = -2}}}

16. Solve for x:
{{{12/(x^2-16) - 3 = 24/(x-4)}}}
{{{(12-3(x^2-16))/(x^2-16) = 24/(x-4)}}} Simplify.
{{{(12-3x^2-48)/(x+4)(x-4) = 24(x+4)/(x-4)(x+4)}}}
{{{12-3x^2-48 = 24x+96}}}
{{{3x^3+24x+36 = 0}}} Simplify by factoring out a 3.
{{{x^2+8x+12 = 0}}} Factor this quadratic equation.
{{{(x+2)(x+6) = 0}}} Apply the zero products principle.
{{{x+2 = 0}}} and/or{{{x+6 = 0}}}
Solutions:
{{{x = -2}}}
{{{x = -6}}}