Differentiate f(x) = (x+3)/(2x-5) using the quotient rule.
For a quotient f(x) = u(x)/v(x), the derivative is f'(x) = (vu'(x) - uv'(x))/v(x)2. Applying this to the given function, we find u(x) = x+3 and v(x) = 2x-5. So, u'(x) = 1 and v'(x) = 2. We can then put these into the expression for the quotient rule: f'(x) = ((2x-5)*1 - (x+3)*2)/(2x-5)2 = (2x - 5 - 2x - 6)/(2x-5)2 = -11/(2x-5)2.
