Question

Subtract the rational expression Please show the steps to the answer

Answer 1

Answer:

$\frac{x^2-8x-12}{2x^2+5x-4}$

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: $\frac{x}{x+3} (\frac{2x -1}{2x-1} ) = \frac{2x^2-x}{2x^2+5x-4}$

• Second term: $\frac{x+4}{2x-1} (\frac{x+3}{x+3} )=\frac{x^2+7x+12}{2x^2+5x-4}$
• Ending expression: $\frac{2x^2-x}{2x^2+5x-4} -\frac{x^2+7x+12}{2x^2+5x-4}$

3. Rewrite terms in a single fraction

$\frac{2x^2-x}{2x^2+5x-4} -\frac{x^2+7x+12}{2x^2+5x-4}$  -----> $\frac{(2x^2-x)-(x^2+7x+12)}{2x^2+5x-4}$

4. Subtract, then combine like terms

Final answer: $\frac{x^2-8x-12}{2x^2+5x-4}$