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1 vote
find the roots of the following equation by factorisation. x+1/x-1- x-1/x+1=5/6: X doesn't equal to 1,-1​

User SirVir
by
8.6k points

2 Answers

1 vote

Answer:

x = -
(1)/(5), x = 5

Explanation:

Given


(x+1)/(x-1) -
(x-1)/(x+1) =
(5)/(6)

Multiply through by 6(x - 1)(x + 1) [ the LCM of the denominators ]

6(x + 1)² - 6(x - 1)² = 5(x - 1)(x + 1) ← expand factors and simplify

6(x² + 2x + 1) - 6(x² - 2x + 1) = 5(x² - 1)

6x² + 12x + 6 - 6x² + 12x - 6 = 5x² - 5

24x = 5x² - 5 ( subtract 24x from both sides )

0 = 5x² - 24x - 5 ← in standard form

0 = (x - 5)(5x + 1) ← in factored form

Equate each factor to zero and solve for x

5x + 1 = 0 ⇒ 5x = - 1 ⇒ x = -
(1)/(5)

x - 5 = 0 ⇒ x = 5

User Suraj Kumar
by
8.6k points
1 vote

Answer:

x= -1/5

hope this helps you

User James Fremen
by
7.8k points
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