Answer:
[tex]\frac{x^2-8x-12}{2x^2+5x-4}[/tex]
1. Find common denominator (LCD)
(x + 3)(2x - 1) = [tex]2x^2 + 5x - 4[/tex]
2. Multiply bottom to get LCD, then multiply top to match
First term: [tex]\frac{x}{x+3} (\frac{2x -1}{2x-1} ) = \frac{2x^2-x}{2x^2+5x-4}[/tex]
- Second term: [tex]\frac{x+4}{2x-1} (\frac{x+3}{x+3} )=\frac{x^2+7x+12}{2x^2+5x-4}[/tex]
- Ending expression: [tex]\frac{2x^2-x}{2x^2+5x-4} -\frac{x^2+7x+12}{2x^2+5x-4}[/tex]
3. Rewrite terms in a single fraction
[tex]\frac{2x^2-x}{2x^2+5x-4} -\frac{x^2+7x+12}{2x^2+5x-4}[/tex] -----> [tex]\frac{(2x^2-x)-(x^2+7x+12)}{2x^2+5x-4}[/tex]
4. Subtract, then combine like terms
Final answer: [tex]\frac{x^2-8x-12}{2x^2+5x-4}[/tex]
