Question

Find the difference. (9/x^2-9x)-(6/x^2-81)

Answer 1

The difference is
`$(3 x+81)/(x(x-9)(x+9))$`

Step-by-step explanation:

The expression is
`$\left((9)/(x^(2)-9 x)\right)-\left((6)/(x^(2)-81)\right)$`

Removing the parenthesis, we have,

`$\left(9)/(x^(2)-9 x)\right-\left(6)/(x^(2)-81)\right$`

Factoring the terms
`$x^(2)-9 x$` and
`$x^(2)-81$`, we get,

`$(9)/(x(x-9))-(6)/((x+9)(x-9))$`

Taking LCM, we get,

`$(9(x+9)-6x)/(x(x-9)(x+9))}$`

Simplifying the numerator, we get,

`$(9x+81-6x)/(x(x-9)(x+9))}$`

Subtracting the numerator, we have,

`$(3 x+81)/(x(x-9)(x+9))$`

Hence, the difference is
`$(3 x+81)/(x(x-9)(x+9))$`