Answer:
(2x + 1) / (2x + 6)
Explanation:
First, factor the numerator (the one in bold):
(2x² - 5x - 3) / (2x² - 18)
= (2x - 6) (2x + 1)/2 / (2x² - 18)
= 2 (x - 3) (2x + 1)/2 / (2x² - 18)
= (x - 3) (2x + 1) / 2x² - 18
= (x - 3) (2x + 1) / 2(x² - 9)
Second, factor the denumerator:
= (x - 3) (2x + 1) / 2(x² - 9)
= (x - 3) (2x + 1) / 2(x + 3) (x - 3)
Third, cross out the similar function between numerator and denumerator:
= (x - 3) (2x + 1) / 2(x + 3) (x - 3)
= 2x + 1 / 2(x + 3)
= (2x + 1) / (2x + 6)
Hope it helps. Thanks!