Question 1126015
<br>
{{{(7/(x-7))+(3/(x+2))=(9x)/(x^2-5x-14)}}}<br>
x=7 and x=-2 are excluded from the domain.<br>
Multiply through by the common denominator and solve:<br>
{{{7(x+2)+3(x-7) = 9x}}}
{{{7x+14+3x-21 = 9x}}}
{{{x = 7}}}<br>
The algebraic solution to the equation is one of the values that is excluded from the domain, so the equation has no solution.<br>
Here is a graph of the DIFFERENCE between the two expressions in the equation; if there were a solution to the equation, this graph would show 0 at some point.<br>
You can see the vertical asymptote at x = -2.  At x=7 there is only a single point "hole" in the graph; this graphing utility does something strange to show it...!<br>
{{{graph(400,400,-20,20,-1,1,(7/(x-7))+(3/(x+2))-(9x)/(x^2-5x-14))}}}