a) \(\displaystyle{{{x^4} + 15x + 7} \over {2{x^3} + 2}}.{x \over {14{x^2} + 1}}.\)\(\displaystyle{{4{x^3} + 4} \over {{x^4} + 15x + 7}}\)
\(\displaystyle = {{\left( {{x^4} + 15x + 7} \right).x.\left( {4{x^3} + 4} \right)} \over {\left( {2{x^3} + 2} \right).\left( {14{x^2} + 1} \right).\left( {{x^4} + 15x + 7} \right)}}\)
\(\displaystyle = {{4x\left( {{x^3} + 1} \right)} \over {2\left( {{x^3} + 1} \right)\left( {14{x^2} + 1} \right)}} = {{2x} \over {14{x^2} + 1}}\)
b) \(\displaystyle{{{x^7} + 3{x^2} + 2} \over {{x^3} - 1}}.{{3x} \over {x + 1}}.{{{x^2} + x + 1} \over {{x^7} + 3{x^2} + 2}}\)\(\displaystyle = {{\left( {{x^7} + 3{x^2} + 2} \right).3x.\left( {{x^2} + x + 1} \right)} \over {\left( {{x^3} - 1} \right)\left( {x + 1} \right)\left( {{x^7} + 3{x^2} + 2} \right)}}\)
\(\displaystyle = {{3x\left( {{x^2} + x + 1} \right)} \over {\left( {x - 1} \right)\left( {{x^2} + x + 1} \right)\left( {x + 1} \right)}} \) \(\displaystyle= {{3x} \over {\left( {x - 1} \right)\left( {x + 1} \right)}}\)
