Question 335132
I presume you mean the following:


{{{(x+4)/(x+5) = (x-2)/(x+4)}}}


If you cross multiply, you get:


{{{(x+4)^2 = (x-2) * (x+5)}}}


If you multiply these out, you will get:


{{{x^2 + 8x + 16 = x^2 + 3x - 10}}}


If  you subtract the expression on the right side of the equation from both sides of the equation, then you will get:


{{{x^2 + 8x + 16 - x^2 - 3x + 10 = x^2 + 3x - 10 - x^2 - 3x + 10}}}


When you combine like terms, you will get:


{{{5x + 26 = 0}}}


If you subtract 26 from both sides of this equation, you will get:


{{{5x = -26}}}


If you divide both sides of this equation by 5, you will get:


x = -26/5


That should be your answer.


Substitute for x in your original equation to see if it comes out true.


You start with {{{(x+4)/(x+5) = (x-2)/(x+4)}}}.


Since -26/5 = -5.2, then you replace x with -5.2 to get:


{{{(-5.2+4)/(-5.2+5) = (-5.2-2)/(-5.2+4)}}}.


This becomes:


{{{(-1.2)/(-.2) = (-7.2)/(-1.2)}}} which becomes:


{{{6 = 6}}} which is true, confirming that your answer of x = -26/5 = -5.2 is correct.