Designing a discrete-time inverse system I am trying to design a discrete-time inverse system to eliminate an undesired echo in a data transmission problem.

The echo caused by the transmission channel is represented as attenuation by a factor of 0.9 and a delay corresponding to one time unit of the input sequence.

The received signal $y[n]$ can be expressed as follow;

$$y[n] = x[n] + 0.9x[n-1]$$

So basically, I'm trying to determine the unit impulse response of a causal inverse system to discover $x[n]$ from $y[n]$.

Conceptually, I'm thinking I need to connect a system $h_2[n]$ in series with the system $h_1[n]$ such that $h_1[n]*h_2[n] = \delta[n]$.

Can anyone offer some advice on how best to go about this ? I've been searching online but can't find a concrete example to use as a starting point.
Correct answer is in the comment already but for completion: Your transfer function is 

$$H(z) = b_0 + b_1 \cdot z^{-1}, \mbox{ with } b_0 = 1, b_1 = .9$$
which makes the inverse
$$H^{-1}(z) = \frac{1}{b_0 + b_1 \cdot z^{-1}} $$
which corresponds to the difference equation
$$y(n) + 0.9 \cdot y(n-1) = x(n) $$ or
$$y(n) = x(n) -0.9 \cdot y(n-1)  $$