Question

Simplify the sum please help and show work

Answer 1

Factoring the second term shows you what the common denominator must be. Then multiply the first term by the appropriate version of 1 and add.

`\displaystyle(4)/(m+9)+(5)/(m^2-81)=(4)/(m+9)+(5)/((m+9)(m-9))\\\\=(4(m-9))/((m+9)(m-9))+(5)/((m+9)(m-9))=(4(m-9)+5)/((m+9)(m-9))\\\\=(4m-36+5)/((m+9)(m-9))\\\\=(4m-31)/((m+9)(m-9))`