Question 153428
Solve for x:
{{{10-13/x = 4 + 5/x}}} Multiply both sides by x.
{{{10x-13 = 4x+5}}} Subtract 4x from both sides.
{{{6x-13 = 5}}} Add 13 to both sides.
{{{6x = 18}}} Finally, divide both sides by 6.
{{{x = 3}}}
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{{{x/(x+4) + 4/(x+4) + 2 = 0}}}  Multiply through by (x+4)
{{{x+4+2(x+4) = 0}}} Expand the last term.
{{{x+4+2x+8 = 0}}} Combine like-terms.
{{{3x+12 = 0}}} Subtact 12 from both sides.
{{{3x = -12}}} Finally, divide both sides by 3.
{{{x = -4}}}
The only problem with this solution is that it is x = -4 is an excluded value.
Why?  Because, when you substitute x = -4 into the original equation, the first two terms are undefined:
{{{-4/(-4+4) + 4/(-4+4) + 2 = 0}}} 
{{{(-4)/0 + 4/0 + 2 = 0}}} As you can see, the first two terms are undefined because division by zero is not defined.