(5)/(x) - (2)/(x-3) = 0
5(x-3) - 2(x) = x(x-3)
5x-15-2x = x^2 -3x
3x-15 = x^2 -3x
this is where i get stuck please help thanks
Let's try it differently.
5/x = 2/(x-3)
5x - 15 = 2x
3x = 15
X = 5
Peter, anything multiplied by zero is still zero,
so your second line should have been
5x-15-2x = 0
Now you have the same as what MatssRiceBowl has in the method he suggested.
To solve the equation 3x - 15 = x^2 - 3x, we need to simplify and rearrange the equation to bring all the terms to one side and set it equal to zero.
1. Start by bringing all terms to the left side of the equation:
x^2 - 3x - 3x + 15 = 0
x^2 - 6x + 15 = 0
2. Now we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = -6, and c = 15.
3. To solve the quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, factoring might not be straightforward, so let's use the quadratic formula.
The quadratic formula is: x = (-b ± √(b^2 - 4ac))/(2a)
Substituting the values for a, b, and c, we get:
x = (-(-6) ± √((-6)^2 - 4(1)(15)))/(2(1))
x = (6 ± √(36 - 60))/2
x = (6 ± √(-24))/2
x = (6 ± √(24)i)/2
x = (6 ± 2√6i)/2
4. Now, we simplify further:
a) x = (6 + 2√6i)/2 = 3 + √6i
b) x = (6 - 2√6i)/2 = 3 - √6i
So, the solution to the equation 3x - 15 = x^2 - 3x is x = 3 + √6i and x = 3 - √6i.
Please note that since we introduced the imaginary unit i (√-1) in the solution, the solutions are complex numbers.