$$\frac{3xy}{2\left(x+z\right)x^{2}}$$

$$\frac{3y}{2x\left(x+z\right)}$$

$$\frac{3y}{2x^{2}+2xz}$$

$$\frac{\left(2zx^{2}+2x^{3}\right)\frac{\mathrm{d}}{\mathrm{d}x}(3yx^{1})-3yx^{1}\frac{\mathrm{d}}{\mathrm{d}x}(2zx^{2}+2x^{3})}{\left(2zx^{2}+2x^{3}\right)^{2}}$$

$$\frac{\left(2zx^{2}+2x^{3}\right)\times 3yx^{1-1}-3yx^{1}\left(2\times 2zx^{2-1}+3\times 2x^{3-1}\right)}{\left(2zx^{2}+2x^{3}\right)^{2}}$$

$$\frac{\left(2zx^{2}+2x^{3}\right)\times 3yx^{0}-3yx^{1}\left(4zx^{1}+6x^{2}\right)}{\left(2zx^{2}+2x^{3}\right)^{2}}$$

$$\frac{2zx^{2}\times 3yx^{0}+2x^{3}\times 3yx^{0}-3yx^{1}\left(4zx^{1}+6x^{2}\right)}{\left(2zx^{2}+2x^{3}\right)^{2}}$$

$$\frac{2zx^{2}\times 3yx^{0}+2x^{3}\times 3yx^{0}-\left(3yx^{1}\times 4zx^{1}+3yx^{1}\times 6x^{2}\right)}{\left(2zx^{2}+2x^{3}\right)^{2}}$$

$$\frac{2z\times 3yx^{2}+2\times 3yx^{3}-\left(3y\times 4zx^{1+1}+3y\times 6x^{1+2}\right)}{\left(2zx^{2}+2x^{3}\right)^{2}}$$

$$\frac{6yzx^{2}+6yx^{3}-\left(12yzx^{2}+18yx^{3}\right)}{\left(2zx^{2}+2x^{3}\right)^{2}}$$

$$\frac{\left(-6yz\right)x^{2}+\left(-12y\right)x^{3}}{\left(2zx^{2}+2x^{3}\right)^{2}}$$