A simply supported beam sits on two supports and carries a load somewhere between them. Statics asks two questions about it, and they are not the same question: how much force does each SUPPORT carry, and how much bending does the BEAM itself feel?

Name the parts once and the rest is bookkeeping. $P$ is the point load in kilonewtons. $L$ is the span, support to support, in metres. $a$ is the distance from the support you are solving at to the load — and the subscript convention matters: $R_A$ is the reaction at support A, and $a$ is measured from A. What is left over, $b = L - a$, is the distance from the load to the far support.

Then $R_A = \dfrac{P(L-a)}{L}$, which is worth reading in words: each support gets the load times the distance to the OTHER support, divided by the span. Put the load close to A and $L - a$ is nearly the whole span, so A takes nearly the whole load. That is the sanity rail for this entire lesson — the near support carries more — and it catches the swapped-distance slip before the arithmetic does. The two reactions always add back to $P$; check it every time, it costs three seconds.

The bending inside the beam peaks directly under the load, at $M = \dfrac{Pa(L-a)}{L}$, in kN·m. Its ceiling is the centred case, $\dfrac{PL}{4}$ — move the load off centre and the beam always feels LESS. Which is why, when a designer does not know where the load will sit, they design for midspan and sleep well.