How do you do x/9 - 8/x = 1/9?

x = -8 or 9

Simplify LHS and move RHS to LHS so that you'll get a quadratic equation, namely, x^2-x-72 = 0 which then gets solved to give the two alternate values of 9 and -8 for x.

it's quite simple:).
Just multiply by x n u have aquadratic function.
x^2/9 - 8 = x/9,
multiply it by 9
x^2 -72 0=x
x^2 + x -72 =0
Factor it
(x+9)(x-8)=0
So the answer is either x=-9 or x=8.
That's all:)

x/9 - 8/x = 1/9

Multiply everything by the common denominator, or 9x

9x^2/9 - 72x/x = 9x/9

Simplify

x^2 - 72 = x

Set equal to 0

x^2 - x - 72 = 0

Factor

(x - 9)(x + 8) = 0

Solve

x = 9, x = -8

Test

x=9
9/9 - 8/9 = 1/9
1/9 = 1/9
TRUE

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

Hope I helped.

Multiply by 9x to simultaneously get rid of the two fractions.
x^2 - 72 = x
x^2 - x - 72 = 0 Yaaay quadratic formula .... or factor in this case is easier
(x - 9)(x + 8)
x = 9, -8

x/9 - 8/x = 1/9
9x(x/9 - 8/x) = 9x(1/9)
x^2 - 72 = x
x^2 - x - 72 = 0
x^2 + 8x - 9x - 72 = 0
(x^2 + 8x) - (9x + 72) = 0
x(x + 8) - 9(x + 8) = 0
(x + 8)(x - 9) = 0

x + 8 = 0
x = -8

x - 9 = 0
x = 9

∴ x = -8 , 9

x ² - 72 = x
x² - x - 72 = 0
(x - 9)(x + 8) = 0
x = 9 , x = - 8

If you multiply both sides of the equation by the Least common denominator, you cancel out all the terms in the denominator.
In this case, the LCD is 9x

9x[x/9 - 8/x] = 9x[1/9]
x²-72=x
x²-x-72=0

you can factor this into
(x-9)(x+8) = 0
x=9 and x=-8

hope this helped :]

multiply through by x and solve the quadratic

x=9

just look at it when subtracting fraction the denominator stays the same and the numerator changes.

so 9/9-8/9=1/9

hope that helped.