Question

Simplify the difference. n^2-10n+24/n^2-13n+42-9/n-7

Answer 1

-17n+12 is the answer

Answer 2

Find the difference of :
`(n^2-10n+24)/(n^2-13n+42) -(9)/(n-7)`

First Factorize the equation:

`n^2-10n+24` as

`n^2-6n-4n+24`

`n(n-6)-4(n-6)`

`(n-6)(n-4)`

Similarly for

`n^2-13n+42` as

`n^2-6n-7n+42`

`n(n-6)-7(n-6)`

`(n-6)(n-7)`

then;

`(n^2-10n+24)/(n^2-13n+42) -(9)/(n-7)`

`((n-6)(n-4))/((n-6)(n-7)) -(9)/(n-7)`

Simplify:

`((n-4))/((n-7)) -(9)/(n-7)`

then;

`(n-4-9)/(n-7) =(n-13)/(n-7)`

therefore, the simplified difference of
`(n^2-10n+24)/(n^2-13n+42) -(9)/(n-7)` is
`(n-13)/(n-7)`