a) \(\displaystyle{{{x^3}} \over {x + 1975}}.{{2x + 1954} \over {x + 1}} \) \(\displaystyle + {{{x^3}} \over {x + 1975}}.{{21 - x} \over {x + 1}}\)
\(\displaystyle = {{{x^3}} \over {x + 1975}}.\left( {{{2x + 1954} \over {x + 1}} + {{21 - x} \over {x + 1}}} \right)\)
\(\displaystyle = {{{x^3}} \over {x + 1975}}.{{x + 1975} \over {x + 1}} \) \(\displaystyle = {{{x^3}\left( {x + 1975} \right)} \over {\left( {x + 1975} \right)\left( {x + 1} \right)}} \) \(\displaystyle = {{{x^3}} \over {x + 1}}\)
b) \(\displaystyle{{19x + 8} \over {x - 7}}.{{5x - 9} \over {x + 1945}} \) \(\displaystyle - {{19x + 8} \over {x - 7}}.{{4x - 2} \over {x + 1945}}\)\(\displaystyle = {{19x + 8} \over {x - 7}}.\left( {{{5x - 9} \over {x + 1945}} - {{4x - 2} \over {x + 1945}}} \right)\)
\(\displaystyle = {{19x + 8} \over {x - 7}}.\left( {{{5x - 9} \over {x + 1945}} + {{2 - 4x} \over {x + 1945}}} \right) \) \(\displaystyle = {{19x + 8} \over {x - 7}}.{{x - 7} \over {x + 1945}}\)
\(\displaystyle = {{\left( {19x + 8} \right)\left( {x - 7} \right)} \over {\left( {x - 7} \right)\left( {x + 1945} \right)}} \) \(\displaystyle = {{19x + 8} \over {x + 1945}} \)
