1. Re arranging an equation.

Ok so i have this equation which I am having difficulty in figuring out how it was derived.

this is the original equation

$\displaystyle \frac{M_s}{P} = L_0 +L_yY +L_rr$

this is the equation i cant figure out how to get to.

$\displaystyle r = \frac{1}{L_r}[\frac{M_s}{P}-L_0] - \frac{L_y}{L_r} Y$

If someone has the time to do a step by step explanation of how to rearrange it to get r, it would help me immensely.

Thanks.

2. Originally Posted by el123
Ok so i have this equation which I am having difficulty in figuring out how it was derived.

this is the original equation

$\displaystyle \frac{M_s}{P} = L_0 +L_yY +L_rr$

this is the equation i cant figure out how to get to.

$\displaystyle r = \frac{1}{L_r}[\frac{M_s}{P}-L_0] - \frac{L_y}{L_r} Y$

If someone has the time to do a step by step explanation of how to rearrange it to get r, it would help me immensely.

Thanks.
(1) $\displaystyle r + \frac{L_yY}{L_r} = \frac{1}{L_r}[\frac{M_s}{P} - L_0]$ First we added to $\displaystyle \frac{L_yY}{L_r}$ both sides

(2) $\displaystyle rL_r + \frac{L_r L_yY}{L_r} = \frac{M_s}{P} - L_0$ Then we multiply both sides by $\displaystyle L_r$ to clear it on the RHS. Note we can cancel these in the second term of the LHS

(3) $\displaystyle rL_r + L_yY + L_0 = \frac{M_s}{P}$ Adding $\displaystyle L_0$ to both sides

You can then rearrange terms to make it look like the answer above.

3. thanks!