# Simplifying Expression in Mathematica

How do I simplify this expression (a result i obtained from previous calculations)

Zin = (R1^2 + R1*RL + 2*L1*R1*s + L1*RL*s + L1^2*s^2 - M^2*s^2)/( R1 + RL + L1 s)


to

Zin = R1 + s*L1 - (s*M)^2/(R1 + RL + s*L1)


I've tried Apart, Cancel, Simplify, FullSimplify, and I can't figure out how to manipulate the equation to get it in the meaningful form I'm looking for.

### Edit

Proof they are identical (after correction) -thank you @bill s

Zin = (R1^2 + R1*RL + 2*L1*R1*s + L1*RL*s + L1^2*s^2 - M^2*s^2)/(R1 + RL + L1 s);

Z2 = R1 + s*L1 - (s*M)^2/(R1 + RL + s*L1);

FullSimplify[Zin == Z2]


True

• Have you considered the possibility that these expressions are not equal, or not equal for all possible complex values of parameters? Have you tried substituting in numbers to check this? May 1 '17 at 21:16
• The two expressions you give are not equivalent. I suggest you check you previous calculations May 1 '17 at 21:17
• Sorry, my mistake ...they are meant to be identical. I messed up the sign infront of the (sM)^2 /(R1+RL+sL1) on the second equation when I transcrbed it from Mathematica to the forum. May 2 '17 at 17:16

The reason it won't simplify to that expression is because they are not equal. Here are your two expressions:

z1 = (R1^2 + R1*RL + 2*L1*R1*s + L1*RL*s + L1^2*s^2 - M^2*s^2)/(R1 + RL + L1 s);
z2 = R1 + s*L1 + (s*M)^2/(R1 + RL + s*L1)
FullSimplify[z1 == z2]
(M s)/(R1 + RL + L1 s) == 0


They are only equal if M s = 0!

• --No...my bad when copying the equations to the forum. Z2 should be R1+sL1-(sM)^2/(R1+RL+s*L1). The expressions are identical (should be, anyway, ;-)). I can't figure out how to get Mathematica to simplify the Z1 expression in your answer to the z2 expression. May 2 '17 at 17:23
Collect[Zin, (s*M)^2, Simplify]


$$\text{R1}+ \text{L1} s -\frac{M^2 s^2}{\text{R1}+\text{RL}+\text{L1} s}$$

• Simple! Thank you. May 3 '17 at 17:47