a) \(\displaystyle {{x + 5} \over {3x - 2}} = {{x\left( {x + 5} \right)} \over {x\left( {3x - 2} \right)}}\)
b. \(\displaystyle {{2x - 1} \over 4}= \frac{{\left( {2x - 1} \right)\left( {2x + 1} \right)}}{{4\left( {2x + 1} \right)}}\)\(\,\displaystyle = {{\left( {2x - 1} \right)\left( {2x + 1} \right)} \over {8x + 4}}\)
c. \(\displaystyle {{2x\left( {x - 2} \right)} \over {{x^2} - 4x + 4}} = \frac{{2x\left( {x - 2} \right)}}{{{x^2} - 2.x.2 + {2^2}}}\)
\(\displaystyle = \frac{{2x\left( {x - 2} \right)}}{{{{\left( {x - 2} \right)}^2}}} = \frac{{2x\left( {x - 2} \right):\left( {x - 2} \right)}}{{{{\left( {x - 2} \right)}^2}:\left( {x - 2} \right)}}\)\(\displaystyle = {{2x} \over {x - 2}}\)
d. \(\displaystyle {{5{x^2} + 10x} \over {\left( {x - 2} \right)\left( {x + 2} \right)}} = \frac{{5x\left( {x + 2} \right)}}{{\left( {x - 2} \right)\left( {x + 2} \right)}} \)
\(\displaystyle = \frac{{5x\left( {x + 2} \right):\left( {x + 2} \right)}}{{\left( {x - 2} \right)\left( {x + 2} \right):\left( {x + 2} \right)}}= {{5x} \over {x - 2}}\)
