To simplify the expression $sinx+sin3x$ / $cosx+cos3x$, we can use the sum-to-product identities for sine and cosine functions.

First, rewrite the expression as:

sinx/cosx + sin3x/cos3x

Now, apply the sum-to-product identity sin$A$ / cos$B$ = tan$A-B$:

tan$x$ + tan$3x$

Now, we can simplify tan$3x$ using the triple angle formula for tangent:

tan$3x$ = $3tan(x)-ta{n}^3(x)$ / $1-3ta{n}^2(x)$

Therefore, the final simplified expression is:

tan$x$ + $3tan(x)-ta{n}^3(x)$ / $1-3ta{n}^2(x)$