(x-3)/5 = (x-3)/x

The x-3 is over the 5 and the other x-3 is over the x...

I know to cross multiply so I would get
5(x-3)= x(x-3) But then would i just divide (x-3) by both sides?

I would assume that's what to do,
but the only reason I ask is because my book says the answer is 3,5

5x-3/5x (x2-3)

To solve the equation (x-3)/5 = (x-3)/x, you have correctly applied the cross-multiplication method.

Starting with 5(x-3) = x(x-3), you can distribute on both sides to simplify the equation:
5x - 15 = x^2 - 3x

Next, bring all the terms to one side to form a quadratic equation:
x^2 - 8x + 15 = 0

Now, you can solve this quadratic equation by factoring or using the quadratic formula.

Let's try factoring:
(x - 3)(x - 5) = 0

To find the values of x, set each factor equal to zero and solve for x:
x - 3 = 0 --> x = 3
x - 5 = 0 --> x = 5

The book says that the answer is 3,5. This means that both x = 3 and x = 5 satisfy the original equation (x-3)/5 = (x-3)/x.

So, the solution to the equation is x = 3, 5.