Question

find the root of the following equation by factorization

x+1/x-1 - x-1/x+1 = 5/6 ; x i not equal to 1 ,-1​

Answer 1

Answer:

Definition: The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Add some parenthesis any where you like!.

Step-by-step explanation:

define of associative property see upp

Answer 2

SOLUTION

TO SOLVE

$\displaystyle \sf{ \frac{x + 1}{x - 1} - \frac{x - 1}{x + 1} = \frac{5}{6} \: \: \: \: \: \: x \ne 1, - 1}$

EVALUATION

$\displaystyle \sf{ \frac{x + 1}{x - 1} - \frac{x - 1}{x + 1} = \frac{5}{6} \: }$

$\displaystyle \sf{ \implies \: \frac{ { (x + 1)}^{2} - {(x - 1)}^{2} }{(x + 1)(x - 1)} = \frac{5}{6} \: }$

$\displaystyle \sf{ \implies \: \frac{ 4.x.1 }{ {x}^{2} - 1} = \frac{5}{6} \: }$

$\displaystyle \sf{ \implies \: \frac{ 4x }{ {x}^{2} - 1} = \frac{5}{6} \: }$

$\displaystyle \sf{ \implies \: 5 {x}^{2} - 5 = 24x \: }$

$\displaystyle \sf{ \implies \: 5 {x}^{2} - 24x - 5 = 0 \: }$

$\displaystyle \sf{ \implies \: 5 {x}^{2} - 25x + x - 5 = 0 \: }$

$\displaystyle \sf{ \implies \: 5x(x - 5) + 1(x - 5) = 0 \: }$

$\displaystyle \sf{ \implies \: (x - 5) (5x + 1) = 0 \: }$

We know that if product of two real numbers are zero then they are separately zero

$\displaystyle \sf{ \implies \: (x - 5) = 0 \: \: or \: \: (5x + 1) = 0 \: }$

Now

$\displaystyle \sf{ (x - 5) = 0 \: \: gives \: \: x = 5\: }$

$\displaystyle \sf{ (5x + 1) = 0 \: \: gives \: \: x = - \frac{1}{5} }$

Hence the required solution is

$\displaystyle \sf{ x = \: \: 5 \: , - \frac{1}{5} }$

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