solve for x if: (x+1÷x-1)-(x-1÷x+1)=5÷6
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Niyathi746:
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(x+1)/(x-1) - (x-1)/(x+1) = 5/6
By taking lcm
[ (x+1)^2 - (x-1)^2 ] / (x-1)(x+1) = 5/6
[ x^2 + 1 + 2x -(x^2 + 1 -2x )] / (x^2 -1) = 5/6
(x^2+1+2x-x^2-1+2x) / (x^2 -1) =5/6
4x/(x^2 -1) = 5/6
By cross multiplying
4x(6) = 5(x^2-1)
24x = 5x^2 -5
5x^2 -24x -5 =0
5x^2 + x- 25x -5 =0
x(5x+1) -5(5x+1) =0
(x-5)(5x+1)=0
x-5=0. Or. 5X+1 =0
x=5. Or. 5X=-1
X=-1/5
•°• The values of x are 1 , -1/5
By taking lcm
[ (x+1)^2 - (x-1)^2 ] / (x-1)(x+1) = 5/6
[ x^2 + 1 + 2x -(x^2 + 1 -2x )] / (x^2 -1) = 5/6
(x^2+1+2x-x^2-1+2x) / (x^2 -1) =5/6
4x/(x^2 -1) = 5/6
By cross multiplying
4x(6) = 5(x^2-1)
24x = 5x^2 -5
5x^2 -24x -5 =0
5x^2 + x- 25x -5 =0
x(5x+1) -5(5x+1) =0
(x-5)(5x+1)=0
x-5=0. Or. 5X+1 =0
x=5. Or. 5X=-1
X=-1/5
•°• The values of x are 1 , -1/5
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