Question

find all values of x that make the equation true
\\(\frac{3}{x - 4}=\frac{x - 5}{x}\\)

Explanation:

Step1: Cross-multiply to eliminate fractions

$$3x = (x-5)(x-4)$$

Step2: Expand the right-hand side

$$3x = x^2 - 9x + 20$$

Step3: Rearrange into quadratic form

$$x^2 - 12x + 20 = 0$$

Step4: Factor the quadratic

$$(x-10)(x-2) = 0$$

Step5: Solve for x

Set each factor equal to 0: $x-10=0$ or $x-2=0$

Answer:

$x=10$ and $x=2$