Question

Subtract the rational expression

Please show the steps to the answer

Answer 1

`(x^2-8x-12)/(2x^2+5x-4)`

1. Find common denominator (LCD)

(x + 3)(2x - 1) =
`2x^2 + 5x - 4`

2. Multiply bottom to get LCD, then multiply top to match

First term:
`(x)/(x+3) ((2x -1)/(2x-1) ) = (2x^2-x)/(2x^2+5x-4)`

• Second term:
  `(x+4)/(2x-1) ((x+3)/(x+3) )=(x^2+7x+12)/(2x^2+5x-4)`
• Ending expression:
  `(2x^2-x)/(2x^2+5x-4) -(x^2+7x+12)/(2x^2+5x-4)`

3. Rewrite terms in a single fraction

`(2x^2-x)/(2x^2+5x-4) -(x^2+7x+12)/(2x^2+5x-4)` ----->
`((2x^2-x)-(x^2+7x+12))/(2x^2+5x-4)`

4. Subtract, then combine like terms

Final answer:
`(x^2-8x-12)/(2x^2+5x-4)`