a: \(\frac{x}{3}=\frac{x\cdot5}{3\cdot5}=\frac{5x}{15}\)
\(\frac{y}{5}=\frac{y\cdot3}{5\cdot3}=\frac{3y}{15}\)
b: \(\frac{2x}{3y}=\frac{2x\cdot x\cdot y}{3y\cdot xy}=\frac{2x^2y}{3xy^2}\)
\(\frac{x+1}{xy^2}=\frac{\left(x+1\right)\cdot3}{xy^2\cdot3}=\frac{3x+3}{3xy^2}\)
c: \(\frac{4}{x^2y}=\frac{4\cdot2\cdot y^2}{x^2y\cdot2y^2}=\frac{8y^2}{2x^2y^3}\)
\(\frac{6}{2xy^3}=\frac{6\cdot x}{2xy^3\cdot x}=\frac{6x}{2x^2y^3}\)
d: \(\frac{3}{\left(x+1\right)^2}=\frac{3\cdot2}{2\left(x+1\right)^2}=\frac{6}{2\left(x+1\right)^2}\)
\(\frac{x}{2\left(x+1\right)}=\frac{x\left(x+1\right)}{2\left(x+1\right)\cdot\left(x+1\right)}=\frac{x^2+x}{2\left(x+1\right)^2}\)
