Combining equations to make one!

Hello this question is based on a transfer function problem and I have the following formulas and need to arrive at an equation for T/V_{D} in terms of k_{0}, k_{1}, k_{2} and k_{t}

where E = V_{D} - V_{M}, I = Ek_{1}, T = k_{0}I, V_{t} = k_{t}T and V_{m} = k_{2}V_{t}

My attempt:

T = k_{0}I where I = Ek_{1 }therefore T = k_{0}Ek_{1} where E = V_{D} - V_{M} hence T = K_{0}(V_{D} - V_{M})K_{1}

Also we know that T = V_{t}/k_{t} where V_{t} = V_{M}/k_{2 }therefore T = V_{M}/(k_{2}k_{t)} hence V_{M }= Tk_{2}k_{t }and substituting V_{M }= Tk_{2}k_{t} into T = K_{0}(V_{D} - V_{M})K_{1}

we have T = K_{0}(V_{D} - Tk_{2}k_{t})K_{1} expanding brackets: T = K_{0}K_{1}V_{D} - K_{0}k_{1}Tk_{2}k_{t }I've tried various rearragements of this but don't seem to come up with T/V_{D }can anyone show me where I'm going wrong?

I'm really stuck

Thanks!

Re: Combining equations to make one!

$\displaystyle \frac{T}{V_D}=\frac{k_0 \cdot I}{E+V_M}=\frac{k_0 \cdot I}{\frac{I}{k_1}+k_2 \cdot V_t}=\frac{k_0 \cdot I}{\frac{I}{k_1}+k_2 \cdot k_t \cdot T}=$

$\displaystyle =\frac{k_0 \cdot I}{\frac{I}{k_1}+k_2 \cdot k_t \cdot k_0 \cdot I}=\frac{k_0}{\frac{1}{k_1}+k_2 \cdot k_t \cdot k_0}=\frac{k_1 \cdot k_0}{1+k_1 \cdot k_2 \cdot k_t \cdot k_0}$

Re: Combining equations to make one!

Got it now, thanks for your help!