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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
5.2k points
1 vote
answer
x=5/3
alternative form
x=1/2/3, x=1.6
User Manuel Fedele
by
5.5k points