What is the product of all valid solutions of the fractional equation
x/(45-5x)=1/[5(x-1)]
I am guessing the answer is -9 because the two solutions would be -3 and 3 but Im not sure.
Don't "guess" in mathematics, it is a precise language, be sure.
x/(45-5x)=1/[5(x-1)]
x/(5(9-x)) = 1/(5(x-1))
multiply by 5
x/(9-x) = 1/(x-1)
multiply both sides by (x-1)(9-x)
x^2 - x = 9 - x
x^2 = 9
x = ± 3
so the product of the solutions is -9