# Find $A$ and $G$ value to satisfy the requirement

Given a disturbance reduction system

Create a system that will reduce $$U(s)$$ noise to $$100$$ times its value. Find the A and G gain value to satisfy the requirement

My attempt: I've analyzed the system and here's what I got

$$Y(s) = \frac{A\cdot H(s) + U(s)}{1+(A\cdot H(s) + U(s) )G(s)} X(s)$$

I don't know what to do next. Any clue? Thanks in advance

Update

Here's what I got after digesting Hilmar's comment: $$Y(s) = \frac{A\cdot H(s)}{1+A\cdot H(s)G(s)}X(s) + \frac{1}{1+A\cdot H(s)G(s)}U(s)$$

Since we want to reduce the noise without sacrificing the $$X(s)$$ signal $$\frac{A\cdot H(s)}{1+A\cdot H(s)G(s)}=1...(1)$$ $$\frac{1}{1+A\cdot H(s)G(s)}=\frac{1}{100}...(2)$$ Then $$1+A\cdot H(s)G(s) = 100$$ Subtituting to the first equation $$A\cdot H(s)=100\\ A = \frac{100}{H(s)}$$ Then $$G(s) = 99$$ How can I get the A value?