Question

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

Answer 1

`(n^2-5n+2)/(2(n-5)(n+5))`

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))`