\(1)\ \frac{1}{3a}=\frac{1\cdot{b}}{3a\cdot{b}}=\frac{b}{3ab}\)
\(\phantom{1)\ }\frac{2}{3b}=\frac{2\cdot{a}}{3b\cdot{a}}=\frac{2a}{3ab};\)
\(2)\ \frac{4m}{p^3q^2}=\frac{4m\cdot{q}}{p^3q^2\cdot{q}}=\frac{4mq}{p^3q^3}\)
\(\phantom{2)\ }\frac{3n}{p^2q^3}=\frac{3n\cdot{p}}{p^2q^3\cdot{p}}=\frac{3np}{p^3q^3};\)
\(3)\ \frac{5}{m-n}=\frac{ 5(m+n)}{ (m-n)(m+n)}=\frac{5m+5n}{m^2-n^2}\)
\(\phantom{3)\ }\frac{6}{m+n}=\frac{ 6(m-n)}{ (m+n)(m-n)}=\frac{6m-6n}{m^2-n^2};\)
\(4)\ \frac{6x}{x-2y}=\frac{ 6x(x+y)}{ (x-2y)(x+y)}=\frac{6x^2+6xy}{x^2+xy-2xy-2y^2}=\frac{6x^2+6xy}{x^2-xy-2y^2}\)
\(\phantom{4)\ }\frac{y}{x+y}=\frac{ y(x-2y)}{ (x+y)(x-2y)}=\frac{xy-2y^2}{x^2+xy-2xy-2y^2}=\frac{xy-2y^2}{x^2-xy-2y^2};\)
\(5)\ \frac{y}{6y-36}=\frac{y}{ 6(y-6)}=\frac{ y\cdot{y}}{ 6(y-6)\cdot{y}}=\frac{y^2}{6y^2-36y}\)
\(\phantom{5)\ }\frac{1}{y^2-6y}=\frac{1}{ y(y-6)}=\frac{1\cdot6}{ y(y-6)\cdot6}=\frac{6}{6y^2-36y};\)
\(6)\ \frac{1}{a^2-1}=\frac{1}{ (a-1)(a+1)}=\frac{1\cdot{a}}{ (a-1)(a+1)\cdot{a}}=\frac{a}{ a(a^2-1)}=\frac{a}{a^3-a}\)
\(\phantom{6)\ }\frac{1}{a^2+a}=\frac{1}{ a(a+1)}=\frac{1\cdot(a-1)}{ a(a+1)(a-1)}=\frac{a-1}{ a(a^2-1)}=\frac{a-1}{a^3-a}.\)
