Simplify the following:
(x+3)/(2 x^2+5 x-3)
Factor the quadratic 2 x^2+5 x-3. The coefficient of x^2 is 2 and the constant term is -3. The product of 2 and -3 is -6. The factors of -6 which sum to 5 are -1 and 6. So 2 x^2+5 x-3 = 2 x^2+6 x-x-3 = 3 (2 x-1)+x (2 x-1):
(x+3)/3 (2 x-1)+x (2 x-1)
Factor 2 x-1 from 3 (2 x-1)+x (2 x-1):
(x+3)/(2 x-1) (x+3)
(x+3)/((2 x-1) (x+3)) = (x+3)/(x+3)×1/(2 x-1) = 1/(2 x-1):
Answer: |
| 1/(2 x-1)
