Answer: The sum will be given as
[tex]1+\frac{6x+20}{x^2-25}[/tex]
Step-by-step explanation:
Since we have given that
[tex]\frac{x^2+6x-5}{x^2-25}[/tex]
We just need to simplify and get the sum :
[tex]\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}x^2+6x-5\mathrm{\:and\:the\:divisor\:}x^2-25\mathrm{\::\:}\frac{x^2}{x^2}=1\\\\\mathrm{Quotient}=1\\\\\mathrm{Multiply\:}x^2-25\mathrm{\:by\:}1:\:x^2-25\\\\\mathrm{Subtract\:}x^2-25\mathrm{\:from\:}x^2+6x-5\mathrm{\:to\:get\:new\:remainder}\\\\\mathrm{Remainder}=6x+20\\\\\frac{x^2+6x-5}{x^2-25}=1+\frac{6x+20}{x^2-25}[/tex]
Hence, the sum will be given as
[tex]1+\frac{6x+20}{x^2-25}[/tex]
