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

Answers

Answer 1
answer
x=5/3
alternative form
x=1/2/3, x=1.6
Answer 2
Answer:     x = ⁵/₃;    x = 5

Step-by-step 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

 


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Step-2 : Find two factors of  8  whose sum equals the coefficient of the middle term, which is   -6 .

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Answers

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Step-by-step explanation:

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