solve for x?

Question

Solve for X

[9/x-5] – 1 = [8/x+5]

Answer 1

[9/x-5] – 1 = [8/x+5]

Assuming you mean by this
[ 9 / (x-5) ] – 1 = [ 8 / (x+5) ]:

Multiply both sides by (x+5)(x-5)
[9/x-5](x+5)(x-5) – (x+5)(x-5) = [8/x+5](x+5)(x-5)
(9)(x+5) - (x+5)(x-5) = (8)(x-5)

9x + 45 - (x² -25) = 8x - 40

Multiply each side by -1, then combine like terms:
x² -9x -70 = -8x + 40
x² -x -110 = 0
(x-11)(x+10) = 0

x = 11 or -10

Answer 2

[9/x - 5] - 1 = [8/x + 5)

(x - 5)(x + 5)(9/x - 5) - (x - 5)(x + 5 = (x - 5)(x + 5)(8/x + 5)

9(x + 5) - (x² - 25) = 8(x - 5)

9x + 45 - x² + 25 = 8x - 40

Combining like terms

- x² + 9x + 45 + 25 = 8x - 40

- x² + 9x + 70 = 8x - 40

- x² + 9x + 70 - 8x = 8x - 40 - 8x

- x² + x + 70 = - 40

- x² + x + 70 + 40 = - 40 + 40

- x² + x + 110 = 0

Multiply the equation y - 1 to make the x² positive

- 1(-x²) + (- 1)(x) + (- 1)(110) = - 1(0)

- ( - x²) + (- x) + ( - 110) = 0

x² - x - 110 = 0

The middle term is - x

x = 1

Find the sum of the middle term

multiply the first term 1 times the last term 110 equals 110 and factor

The factors of 110 =

1 x 110
2 x 55
5 x 22
10 x 11. . .<=. .use these factors

- 11 and + 10 satisfy the sum of the middle term

Insert - 11x and + 10x into the equation

x² - x - 110 = 0

x² - 11x + 10x - 110 = 0

x(x - 11) + 10(x - 11) = 0

(x + 10)(x - 11) = 0

- - - - - - - -s-

Answer 3

Question should be:-
9 / (x - 5) - 1 = 8 / (x + 5)
9.(x + 5) - 1.(x - 5).(x + 5) = 8.(x - 5)
9x + 45 - 1.(x² - 25) = 8x - 40
9x + 45 - x² + 25 = 8x - 40
x + 110 - x² = 0
x² - x - 110 = 0
(x - 11).(x + 10) = 0
x = 11, x = - 10

Answer 4

9/x - 5 -1 = 8/x +5

9/x - 8/x -6 = 5
1/x = 11

x = 1/11

Answer 5

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