+188 I'm going to assume you mean x / ( x - 5 ) = 4 / ( x - 4 ).
From that equation, we can cross multiply and get x ( x - 4 ) = 4 ( x - 5 ).
Expand. x^2 - 4x = 4x - 20.
To make it easier to find all values of x, set the equation equal to zero. x^2 - 8x + 20 = 0.
Plugging this into the Quadratic Formula, we get x = [ 8 ± sqrt ( 64 - 4 * 1 * 20 ) ] / ( 2 * 1 ).
Simplify. x = 4 ± 2i.
(Simplifiying steps:
1. Simplify the inside of the square root: x = [ 8 ± sqrt ( -16 ) ] / ( 2 * 1 )
2. Simplify the denominator: x = [ 8 ± sqrt ( -16 ) ] / 2
3. Separate the fraction two parts: x = ( 8 / 2 ) ± [ ( sqrt -16 ) / 2 ]
4. Simplify the two fractions: x = 4 ± 2i
(Basically doing 8 / 2, and solving the imaginary fraction ( ( i * sqrt 16 ) / 2 = 4i / 2 = 2i ) )
I hope I helped! A bit rusty on this topic, so if I made any mistake please lmk!
