1. Draw the asymptotes and mark those parts of the coordinate system where the graph of the function never can be.

2. Draw a smooth curve to the asymptotes in the "allowed" areas.

3. From the vertical asymptote you know that the denominator must contain the factor (x+1).

From the horizontal asymptote you know that the numerator must contain the factor (2x+3).

4. I've sketched the function which obviously satisfies all given conditions.