a: \(\frac{5}{x^5y^3}=\frac{5\cdot12\cdot y}{x^5y^3\cdot12y}=\frac{60y}{12x^5y^4}\)
\(\frac{7}{12x^3y^4}=\frac{7\cdot x^2}{12x^3y^4\cdot x^2}=\frac{7x^2}{12x^5y^4}\)
b: \(\frac{4}{15x^3y^5}=\frac{4\cdot4\cdot x}{15x^3y^5\cdot4x}=\frac{16x}{60x^4y^5}\)
\(\frac{11}{12x^4y^2}=\frac{11\cdot5\cdot y^3}{12x^4y^2\cdot5y^3}=\frac{55y^3}{60x^4y^5}\)
c: \(\frac{5}{2x+6}=\frac{5}{2\left(x+3\right)}=\frac{5\cdot\left(x-3\right)}{2\left(x+3\right)\left(x-3\right)}=\frac{5x-15}{2\left(x+3\right)\left(x-3\right)}\)
\(\frac{3}{x^2-9}=\frac{3}{\left(x-3\right)\left(x+3\right)}=\frac{3\cdot2}{2\cdot\left(x-3\right)\left(x+3\right)}=\frac{6}{2\left(x-3\right)\left(x+3\right)}\)
d: \(\frac{3x}{2x+4}=\frac{3x}{2\left(x+2\right)}=\frac{3x\cdot\left(x-2\right)}{2\left(x+2\right)\left(x-2\right)}=\frac{3x^2-6x}{2\left(x+2\right)\left(x-2\right)}\)
\(\frac{x+3}{x^2-4}=\frac{x+3}{\left(x-2\right)\left(x+2\right)}=\frac{2\cdot\left(x+3\right)}{2\left(x-2\right)\left(x+2\right)}=\frac{2x+6}{2\left(x-2\right)\left(x+2\right)}\)
