\(1)\ \frac{1}{8ab}=\frac{1\cdot{a^2}}{8ab\cdot{a^2}}=\frac{a^2}{8a^3b}\)
\(\phantom{1)\ }\frac{1}{2a^3}=\frac{1\cdot4b}{2a^3\cdot4b}=\frac{4b}{8a^3b};\)
\(2)\ \frac{3x}{7m^3n^3}=\frac{3x\cdot3n}{7m^3n^3\cdot3n}=\frac{9nx}{21m^3n^4}\)
\(\phantom{2)\ }\frac{4y}{3m^2n^4}=\frac{4y\cdot7m}{3m^2n^4\cdot7m}=\frac{28my}{21m^3n^4};\)
\(3)\ \frac{a+b}{a-b}=\frac{ (a+b)(a+b)}{ (a-b)(a+b)}=\frac{ (a+b)^2}{a^2-b^2}=\frac{a^2+2ab+b^2}{a^2-b^2}\)
\(\phantom{3)\ }\frac{2}{a^2-b^2};\)
\(4)\ \frac{3d}{m-n}=\frac{ 3d(m-n)}{ (m-n)(m-n)}=\frac{3dm-3dn}{ (m-n)^2}=\frac{3dm-3dn}{m^2-2mn+n^2}\)
\(\phantom{4)\ }\frac{8p}{ (m-n)^2}=\frac{8p}{ (m-n)(m-n)}=\frac{8p}{m^2-2mn+n^2};\)
\(5)\ \frac{x}{2x+1}=\frac{ x(3x-2)}{ (2x+1)(3x-2)}=\frac{3x^2-2x}{6x^2-4x+3x-2}=\frac{3x^2-2x}{6x^2-x-2}\)
\(\phantom{5)\ }\frac{x}{3x-2}=\frac{ x(2x+1)}{ (3x-2)(2x+1)}=\frac{2x^2+x}{6x^2-4x+3x-2}=\frac{2x^2+x}{6x^2-x-2};\)
\(6)\ \frac{a-b}{3a+3b}=\frac{a-b}{ 3(a+b)}=\frac{ (a-b)(a-b)}{ 3(a+b)(a-b)}=\frac{ (a-b)^2}{ 3(a^2-b^2)}=\frac{a^2-2ab+b^2}{3a^2-3b^2}\)
\(\phantom{6)\ }\frac{a}{a^2-b^2}=\frac{a}{ (a-b)(a+b)}=\frac{3a}{ 3(a-b)(a+b)}=\frac{3a}{ 3(a^2-b^2)}=\frac{3a}{3a^2-3b^2};\)
\(7)\ \frac{3a}{4a-4}=\frac{3a}{ {-}4(1-a)}={-}\frac{3a\cdot5}{ 4(1-a)\cdot5}={-}\frac{15a}{20-20a}\)
\(\phantom{7)\ }\frac{2a}{5-5a}=\frac{2a}{ 5(1-a)}=\frac{2a\cdot4}{ 5(1-a)\cdot4}=\frac{8a}{20-20a};\)
\(8)\ \frac{7a}{b-3}=\frac{7a}{ {-}(3-b)}={-}\frac{ 7a\cdot(3+b)}{ (3-b)\cdot(3+b)}={-}\frac{21a+7ab}{9-b^2}\)
\(\phantom{8)\ }\frac{c}{9-b^2}.\)
