# How to simplify an expression to a variable?

So I'm doing some operations in Mathematica and I arrive to this expression:

Clear[ZC1, s, CC1, ZCR1, R1, KVL1, V1, I1, V2, I2, KVL2, R2, param, a, b, c, d, cond, aux, Tran1RC, Tran2RC,
R3, R4, CC3, Circuito, gain, Tfilter];

ZC1 = 1/(s*CC1)

ZCR1 = Simplify[(R1*ZC1)/(R1 + ZC1)]

KVL1 = V1 == ZCR1*I1 + V2;

KVL2 = V2 == R2*(I1 + I2);

param = a == V1/V2;

cond = I2 == 0;

aux = Solve[KVL1 && KVL2 && param && cond, {a, V1, V2, I2}]

a = a /. aux[[1]][[1]]

param = b == -(V1/I2);

cond = V2 == 0;

aux = Solve[KVL1 && KVL2 && param && cond, {b, V1, V2, I2}]

b = b /. aux[[1]][[1]]

param = c == I1/V2;

cond = I2 == 0;

aux = Solve[KVL1 && KVL2 && param && cond, {c, I1, V2, I2}]

c = c /. aux[[1]][[1]]

param = d == -(I1/I2);

cond = V2 == 0;

aux = Solve[KVL1 && KVL2 && param && cond, {d, I1, I2, V2}]

d = d /. aux[[1]][[1]]

Tran1RC = {{a, b}, {c, d}};

Tran1RC // MatrixForm

a = a /. {R1 -> R3, R2 -> R4, CC1 -> CC3}

b = b /. {R1 -> R3, R2 -> R4, CC1 -> CC3}

c = c /. {R1 -> R3, R2 -> R4, CC1 -> CC3}

d = d /. {R1 -> R3, R2 -> R4, CC1 -> CC3}

Tran2RC = {{a, b}, {c, d}};

Tran2RC // MatrixForm

Circuito = Simplify[Tran1RC.Tran2RC];

Circuito // MatrixForm

gain = Circuito[[1]][[1]] /. {CC3 -> 10 CC1, R2 -> R3 + R4}

Tfilter = Simplify[1/gain]

Now the final expression I want to simplify according to variable s meaning that I want to arrive with expression in powers of s (s^1 and s^2) both in the numerator and the denominator. Exactly how shall I do this?

EDIT: Put the full workable code

• You should write your code. Not just copy an image. With your code will be more easy to help you. Aug 21, 2020 at 15:53
• @Cruz what difference does it make? What do you need more? Aug 21, 2020 at 15:54
• I think Expand[Together[your expression]] will do it, but it's too much work to try it out when you haven't posted copyable code. Aug 21, 2020 at 16:00
• Because it's polite to help us help you. Instead of expecting us to re-type your code, we can copy and paste what's in your post into our own copies of Mathematica, expediting any help you might get! Aug 21, 2020 at 16:01
• @march you are right, I just assumed it was an easy thing to answer for people that are use Mathematica frequently. Anyway, how do I post code easily? Does Mathematica have an export code option? Thank you in advance for your help Aug 21, 2020 at 16:10

Rfilter = Together[Tfilter];
Collect[Numerator[Rfilter], s]/Collect[Denominator[Rfilter], s]

yielding

(R3 R4 + R4^2 +
(CC1 R1 R3 R4 + 10 CC1 R3^2 R4 + CC1 R1 R4^2 + 10 CC1 R3 R4^2) s +
(10 CC1^2 R1 R3^2 R4 + 10 CC1^2 R1 R3 R4^2) s^2)
/
(2 R1 R3 + R3^2 + 2 R1 R4 + 2 R3 R4 +
R4^2 +
(11 CC1 R1 R3^2 + 22 CC1 R1 R3 R4 + 10 CC1 R3^2 R4 + CC1 R1 R4^2 + 10 CC1 R3 R4^2) s +
(10 CC1^2 R1 R3^2 R4 + 10 CC1^2 R1 R3 R4^2) s^2)