72.3k views
2 votes
Find the value of x in the rational equation below. The answer must be an exact value.

(20)/(x^2-25)=(-3)/(5-x)
Thank You

2 Answers

4 votes

Answer: x = ⁵/₃; x = 5

Explanation:

Since (20) = (-3) [we can cross multiply]

(x²- 25) (5-x)

⇒ (20)(5 - x) = (-3)(x² - 25) [expand the brackets]

⇒ 100 - 20x = -3x² + 75 [make the equation equal to zero]

⇒ 3x² - 20x + 25 = 0 [expand the middle term using

appropriate factors of the product

of the terms a and c (3 × 25)]

⇒ 3x² - 15x - 5x + 25 = 0 [factorize the terms]

⇒ (3x - 5 ) (x - 5) = 0 [using the knowledge that for the

produc to be 0, one of terms

must be zero]

⇒ (3x - 5 ) = 0 OR (x - 5) = 0 [solve for x in each case]

⇒ x = ⁵/₃ OR x = 5

User Mike Yockey
by
7.7k points
1 vote
answer
x=5/3
alternative form
x=1/2/3, x=1.6
User Manuel Fedele
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories