# How do you simplify #n/(2n+10)+1/(n^2-25)#?

##### 1 Answer

Jul 3, 2017

#### Explanation:

#"before we can add the fractions we require them to have"#

#"a "color(blue)"common denominator"#

#"first factorise the denominators"#

#rArrn/(2(n+5))+1/((n-5)(n+5))larrcolor(blue)" difference of squares"#

#"multiply the numerator/denominator of the fraction on the "#

#" left by " (n-5)#

#"multiply the numerator/denominator of the fraction on the"#

#"right by " 2#

#rArr(n(n-5))/(2(n+5)(n-5))+(2)/(2(n+5)(n-5))#

#"now the denominators are common we can add the numerators"#

#"leaving the denominator as it is."#

#rArr(n^2-5n+2)/(2(n+5)(n-5))#

#=(n^2-5n+2)/(2(n+5)(n-5))#