Because you are asking about rational equations, I read this asâ€¦
4 = 10 + 3
--- ---- ----
3x 3 x
which greatly affects the answer.
Multiply everything by 3x to get the same denominator across the board.
4 = 10x + 9
Now, itâ€™s just a simple equationâ€¦ not quadratic.
Subtract 9 from both sides.
-5 = 10x
Divide by 10.
x = -5/10 = -1/2
Plug back into your original problem to make sure it will NOT make any denominator 0, which it doesnâ€™t. Valid solution, check!