x-5 divided by 2 = x-3 divided by x
x(x-5) = 2(x-3)
x^-5x=2x-6
x^ -7x +6 =0
(x+1) (x-6)
x=-1
x=6
x^2 - 7x + 6 = 0
(x-1)(x-6) = 0
x = 1
x = 6
To solve the equation (x-5)/2 = (x-3)/x, we need to cross-multiply and simplify:
(x-5)/2 = (x-3)/x
Cross-multiplying gives:
x(x-5) = 2(x-3)
Expanding both sides:
x^2 - 5x = 2x - 6
Rearranging the equation:
x^2 - 7x + 6 = 0
Factoring the quadratic equation gives us:
(x+1)(x-6) = 0
Setting each factor equal to zero gives us two possible solutions:
x + 1 = 0 or x - 6 = 0
Simplifying each equation:
x = -1 or x = 6
Therefore, the solutions to the equation (x-5)/2 = (x-3)/x are x = -1 and x = 6.