Question

Simplify
`(1)/(X-10)` ÷
`(9X)/(x^(2)- 9x -10)`

Answer 1

In the second fraction, factorize the denominator:

`x^2-9x-10=(x-10)(x+1)`

Then we have, as long as
`x\\eq10`,

`\frac1{x-10}/(9x)/(x^2-9x-10)=\frac{\frac1{x-10}}{(9x)/((x-10)(x+1))}=\frac1{(9x)/(x+1)}=(x+1)/(9x)`

which you could also write as

`(x+1)/(9x)=\frac x{9x}+\frac1{9x}=\frac19+\frac1{9x}`