Solve (x)/(1) - 5/x = 4 ... step by step = best answer

x- 5/x = 4

multiplt through by x gives

x² -5 = 4x
rearange

x² - 4x - 5=0

factorise

(x - 5)( x + 1) = 0

either (x - 5) = 0 so x = 5

or (x + 1 ) = 0 so x = - 1

Add 5/x to both sides:
x/1 = 4 + 5/x

Subtract 4 from both sides:
x - 4 = 5/x

Multiply both sides by x:
x(x - 4) = 5

Expand x(x - 4) = 5:
x^2 - 4x = 5

Subtract 5 from both sides:
x^2 - 4x - 5 = 0

Use the quadratic equation to solve for x, or factor:
(x - 5)(x + 1) = 0

Two numbers multiplied together equal zero only if at least one of those numbers equals zero.
(x - 5) = 0 or (x + 1) = 0
x = 5 or x = -1

The trick to problems like this one is to isolate u/x to one side of the equals sign, where u is some real number, and then you can multiply both sides by x to get a quadratic.
As long as you don't divide anything by zero, the algebra will work.

x/1-5/x
x-5/x=4 mult whol equation x to get rid of fraction
x^2-5x=4x add 5x toboth sides

x^2=9x div by 9

x^2)/9=x

x/1 - 5/x = 4

Get the LCD..
x^2 - 5/x = 4

[(x^2 - 5)/x = 4] x

x^2 - 5 = 4x

x^2 - 4x - 5 = 0

(x-5) (x+1) = 0

x = 5 ; x = -1