Question

Need help please show work

Answer 1

Part 1:
`(3-x)/((x+3)(x-4))`

Explanation:

`(-3)/(x-4) + (2x+12)/(x^2-x-12)`

First, factor the denominator of the second term.

`x^2-x-12 = (x+3)(x-4)`

↓

`(-3)/(x-4) + (2x+12)/((x+3)(x-4))`

Next, multiply the first term by
`(x+3)/(x+3)` to give both terms a common denominator:

`\left((x+3)/(x+3) \right) \left( (-3)/(x-4) \right) + (2x+12)/((x+3)(x-4))`

`(-3(x+3))/((x+3)(x-4)) + (2x+12)/((x+3)(x-4))`

and combine the terms.

`(-3(x+3) + 2x + 12)/((x+3)(x-4))`

Finally, simplify the numerator:

`(-3x-9 + 2x + 12)/((x+3)(x-4))`

`(3-x)/((x+3)(x-4))`