Đáp án:

$\begin{array}{l}
a)\dfrac{{7x + 11}}{{2x + 14}} - \dfrac{{3x + 2}}{{x + 7}}\\
 = \dfrac{{7x + 11 - 2.\left( {3x + 2} \right)}}{{2.\left( {x + 7} \right)}}\\
 = \dfrac{{7x + 11 - 6x - 4}}{{2\left( {x + 7} \right)}}\\
 = \dfrac{{x + 7}}{{2\left( {x + 7} \right)}}\\
 = \dfrac{1}{2}\\
b)\\
\dfrac{{4x}}{{x - 1}} + \dfrac{{3x}}{{x + 1}} - 7\\
 = \dfrac{{4x\left( {x + 1} \right) + 3x\left( {x - 1} \right) - 7\left( {{x^2} - 1} \right)}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}\\
 = \dfrac{{4{x^2} + 4x + 3{x^2} - 3x - 7{x^2} + 7}}{{{x^2} - 1}}\\
 = \dfrac{{x + 7}}{{{x^2} - 1}}\\
c)\dfrac{{2x + 1}}{{2x + 2}} - \dfrac{{2x - 2}}{{2x - 1}} + \dfrac{{3x}}{{2\left( {x + 1} \right)\left( {2x - 1} \right)}}\\
 = \dfrac{{\left( {2x + 1} \right)\left( {2x - 1} \right) - \left( {2x - 2} \right)\left( {2x + 2} \right) + 3x}}{{2\left( {x + 1} \right)\left( {2x - 1} \right)}}\\
 = \dfrac{{4{x^2} - 2x + 2x - 1 - 4\left( {{x^2} - 1} \right) + 3x}}{{2\left( {x + 1} \right)\left( {2x - 1} \right)}}\\
 = \dfrac{{4{x^2} - 1 - 4{x^2} + 1 + 3x}}{{2\left( {x + 1} \right)\left( {2x - 1} \right)}}\\
 = \dfrac{{3x}}{{2\left( {x + 1} \right)\left( {2x - 1} \right)}}\\
d)\dfrac{1}{{x - 2}} - \dfrac{1}{{x + 2}} + \dfrac{{{x^2} + 4x}}{{{x^2} - 4}}\\
 = \dfrac{{x + 2 - \left( {x - 2} \right) + {x^2} + 4x}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\\
 = \dfrac{{x + 2 - x + 2 + {x^2} + 4x}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\\
 = \dfrac{{{x^2} + 4x + 4}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\\
 = \dfrac{{{{\left( {x + 2} \right)}^2}}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\\
 = \dfrac{{x + 2}}{{x - 2}}\\
e)\dfrac{{{x^2} + 2x}}{{2x + 10}} + \dfrac{{x - 5}}{x} - \dfrac{{5x - 50}}{{2{x^2} + 10x}}\\
 = \dfrac{{{x^2} + 2x}}{{2\left( {x + 5} \right)}} + \dfrac{{x - 5}}{x} - \dfrac{{5x - 50}}{{2x\left( {x + 5} \right)}}\\
 = \dfrac{{\left( {{x^2} + 2x} \right).x + \left( {x - 5} \right).2\left( {x + 5} \right) - 5x + 50}}{{2x\left( {x + 5} \right)}}\\
 = \dfrac{{{x^3} + 2{x^2} + 2{x^2} - 50 - 5x + 50}}{{2x\left( {x + 5} \right)}}\\
 = \dfrac{{{x^3} + 4{x^2} - 5x}}{{2x\left( {x + 5} \right)}}\\
 = \dfrac{{x\left( {x + 5} \right)\left( {x - 1} \right)}}{{2x\left( {x + 5} \right)}}\\
 = \dfrac{{x - 1}}{2}\\
f)\dfrac{{x - 1}}{{x + 1}} - \dfrac{{2x}}{{x - 3}} + \dfrac{{{x^2} - 9}}{{{x^2} - 2x - 3}}\\
 = \dfrac{{\left( {x - 1} \right)\left( {x - 3} \right) - 2x\left( {x + 1} \right) + {x^2} - 9}}{{\left( {x + 1} \right)\left( {x - 3} \right)}}\\
 = \dfrac{{{x^2} - 4x + 3 - 2{x^2} - 2x + {x^2} - 9}}{{\left( {x + 1} \right)\left( {x - 3} \right)}}\\
 = \dfrac{{ - 6x - 6}}{{\left( {x + 1} \right)\left( {x - 3} \right)}}\\
 = \dfrac{{ - 6\left( {x + 1} \right)}}{{\left( {x + 1} \right)\left( {x - 3} \right)}}\\
 = \dfrac{{ - 6}}{{x - 3}}\\
 = \dfrac{6}{{3 - x}}
\end{array}$

${a}$ $\dfrac{7x + 11}{2x + 14}$  ${-}$ $\dfrac{3x + 2}{x + 7}$

${=}$ $\dfrac{7x + 11}{2( x + 7 )}$ ${-}$ $\dfrac{3x + 2}{x + 7}$

${=}$ $\dfrac{7x + 11 - 2( 3x + 2 )}{2( x + 7 )}$

${=}$ $\dfrac{7x + 11 - 6x - 4}{2( x + 7 )}$

${=}$ $\dfrac{x + 7}{2( x + 7 )}$

${=}$ $\dfrac{1}{2}$

${b,}$  $\dfrac{4x}{x - 1}$  ${+}$ $\dfrac{3x}{x + 1}$ ${- 7}$

${=}$ $\dfrac{4x( x + 1 ) + 3x( x - 1 ) - 7( x - 1 )( x + 1 )}{( x - 1 )( x + 1 )}$

${=}$ $\dfrac{4x^2 + 4x + 3x^2 - 3x - 7( x^2 - 1 )}{(x^2 - 1}$
${=}$ $\dfrac{4x^2 + 4x + 3x^2 - 3x - 7x^2 +7}{x^2 - 1}$

${=}$ $\dfrac{x + 7}{x^2 - 1}$

${c,}$  $\dfrac{2x + 1}{2x + 2}$  ${-}$ $\dfrac{2x - 2}{2x - 1}$ ${+}$ $\dfrac{3x}{2( x + 1 )( 2x - 1 )}$

${=}$ $\dfrac{2x + 1}{2( x + 1  )}$ ${-}$ $\dfrac{2x - 2}{2x - 1}$ ${+}$ $\dfrac{3x}{2( x + 1 )( 2x - 1 )}$

${=}$ $\dfrac{( 2x - 1 )( 2x + 1 ) - 2( x + 1 )( 2x - 2 )  + 3x}{2( x + 1 )( 2x - 1 )}$

${=}$ $\dfrac{4x^2 - 1 + ( -2x - 2 )( -2 + 2x ) + 3x}{2( x + 1 )( 2x - 1 )}$

${=}$ $\dfrac{4x^2 - 1 + ( -2 - 2x)( -2 + 2x ) + 3x}{2( x + 1 )( 2x - 1 )}$

${=}$ $\dfrac{4x^2 - 1 + 4 - 4x^2 + 3x}{2( x + 1 )( 2x - 1 )}$

${=}$ $\dfrac{3 + 3x}{2( x + 1 )( 2x - 1 )}$

${=}$ $\dfrac{3x + 3}{2( x + 1 )( 2x - 1 )}$

${=}$ $\dfrac{3( x + 1 )}{2( x + 1 )( 2x - 1 )}$

${=}$ $\dfrac{3}{2( 2x - 1 )}$

${=}$ $\dfrac{3}{4x - 2}$

${d,}$ $\dfrac{1}{x - 2}$ ${ - }$ $\dfrac{1}{x + 2}$ ${+}$ $\dfrac{x^2 + 4x}{x^2 - 4}$

${=}$ $\dfrac{1}{x - 2}$ ${ - }$ $\dfrac{1}{x + 2}$ ${+}$ $\dfrac{x^2 + 4x}{( x - 2 )( x + 2 )}$

${=}$ $\dfrac{x + 2 - ( x - 2 ) + x^2 + 4x}{( x - 2 )( x + 2 )}$

${=}$ $\dfrac{x + 2 - x + 2 + x^2 + 4x}{( x - 2 )( x + 2 )}$

${=}$ $\dfrac{4 + x^2 + 4x}{( x - 2 )( x + 2 )}$

${=}$ $\dfrac{4 + 4x + x^2}{( x - 2 )( x + 2 )}$

${=}$ $\dfrac{( 2 + x )^2}{( x - 2 )( x + 2 )}$

${=}$ $\dfrac{2 + x}{x - 2}$

${e,}$ $\dfrac{x^2 + 2x}{2x + 10}$ ${+}$ $\dfrac{x - 5}{x}$ ${-}$ $\dfrac{5x - 50}{2x^2 + 10x}$

${=}$ $\dfrac{x^2 + 2x}{2( x + 5 )}$ ${+}$ $\dfrac{x - 5}{x}$ ${-}$ $\dfrac{5x - 50}{2x( x + 5 )}$

${=}$ $\dfrac{x( x^2 + 2x ) + 2( x + 5 )( x - 5 ) - ( 5x - 50 )}{2x( x + 5 )}$

${=}$ $\dfrac{x^3 + 2x^2 + 2( x^2 - 25 ) - 5x + 50}{2x( x + 5 )}$

${=}$ $\dfrac{x^3 + 2x^2 + 2x^2 - 50 - 5x + 50}{2x( x + 5 )}$

${=}$ $\dfrac{x^3 + 4x^2 - 5x}{2x( x + 5 )}$

${=}$ $\dfrac{x( x^2 + 4x - 5 )}{2x( x + 5 )}$

${=}$ $\dfrac{x^2 + 5x - x - 5}{2( x + 5 )}$

${=}$ $\dfrac{x( x + 5 ) - ( x + 5 )}{2x( x + 5 )}$

${=}$ $\dfrac{( x + 5 )( x - 1 )}{2x( x + 5 )}$

${=}$ $\dfrac{x - 1}{2}$

${f.}$ $\dfrac{x - 1}{x + 1}$ ${-}$ $\dfrac{2x}{x - 3}$ ${+}$ $\dfrac{x^2 - 9}{x^2 - 2x - 3}$

${=}$ $\dfrac{x - 1}{x + 1}$ ${-}$ $\dfrac{2x}{x - 3}$ ${+}$ $\dfrac{( x - 3 )( x + 3 )}{x^2 + x - 3x - 3}$

${=}$ $\dfrac{x - 1}{x + 1}$ ${-}$ $\dfrac{2x}{x - 3}$ ${+}$ $\dfrac{( x - 3 )( x + 3 )}{x( x + 1 ) - 3( x + 1 )}$

${=}$ $\dfrac{x - 1}{x + 1}$ ${-}$ $\dfrac{2x}{x - 3}$ ${+}$ $\dfrac{( x - 3 )( x + 3 )}{( x + 1 )( x - 3 )}$

${=}$ $\dfrac{x - 1}{x + 1}$ ${-}$ $\dfrac{2x}{x - 3}$ ${+}$ $\dfrac{x + 3}{x + 1}$

${=}$ $\dfrac{( x - 3 )( x - 1 ) - 2x( x + 1 ) + ( x - 3 )( x + 3 )}{( x + 1 )( x - 3 )}$

${=}$ $\dfrac{x^2 - x - 3x + 3 - 2x^2 - 2x + x^2 -9}{( x + 1 )( x - 3 )}$

${=}$ $\dfrac{0 -6x - 6}{( x + 1 )( x - 3 )}$

${=}$ $\dfrac{-6( x + 1 )}{( x + 1 )( x - 3 )}$

${=}$ $\dfrac{-6}{( x - 3 )}$