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4 votes
Simplify the Rational Expression
(2x²−5x−3)/(2x²−18)

User Horta
by
8.1k points

1 Answer

3 votes

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!

User Ghazala
by
7.7k points

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