Đề bài
Rút gọn biểu thức :
a] \[{{3{a^2}b} \over {4c}}.{{{c^2}} \over {ab}}\] ;
b] \[{9 \over {d - 3f}}:{6 \over {9f - 3d}}\] ;
c] \[{{10k} \over {k - 5}}.{{3{k^2} - 15k} \over {5{k^2}}}\] ;
d] \[{{4x - 1} \over {4y - 4x}}:{3 \over {9x - 9y}}\] ;
e] \[{{mn - 4m + 2{n^2} - 8n} \over {m + 2n}}:{{4 - n} \over n}\] ;
f] \[{{7{{[p - q]}^2}} \over {pq}}.{{2{p^3}{q^2}} \over {p - {q^2}}}\]
Lời giải chi tiết
\[\eqalign{ & a]\,\,{{3{a^2}b} \over {4c}}.{{{c^2}} \over {ab}} = {{3{a^2}b{c^2}} \over {4cab}} = {{3{a^2}b{c^2}} \over {4abc}} = {{3ac} \over 4} \cr & b]\,\,{9 \over {d - 3f}}:{6 \over {9f - 3d}} = {9 \over {d - 3f}}.{{9f - 3d} \over 6} \cr & \,\,\,\,\, = {9 \over {d - 3f}}.{{ - 3\left[ {d - 3f} \right]} \over 6} = {{ - 9} \over 2} \cr & c]\,\,{{10k} \over {k - 5}}.{{3{k^2} - 15k} \over {5{k^2}}} = {{10k\left[ {3{k^2} - 15k} \right]} \over {\left[ {k - 5} \right]5{k^2}}} \cr & \,\,\,\,\, = {{10k.3k.\left[ {k - 5} \right]} \over {\left[ {k - 5} \right]5{k^2}}} = {{30{k^2}} \over {5{k^2}}} = 6 \cr & d]\,\,{{4x - 1} \over {4y - 4x}}:{3 \over {9x - 9y}} = {{ - \left[ {4x - 1} \right]} \over {4x - 4y}}.{{9x - 9y} \over 3} \cr & \,\,\,\,\, = {{ - \left[ {4x - 1} \right]9\left[ {x - y} \right]} \over {4\left[ {x - y} \right].3}} = {{ - \left[ {4x - 1} \right].3} \over 4} = - {{3\left[ {4x - 1} \right]} \over 4} \cr & e]\,\,{{mn - 4m + 2{n^2} - 8n} \over {m + 2n}}:{{4 - n} \over n} = {{mn - 4m + 2{n^2} - 8n} \over {m + 2n}}.{n \over {4 - n}} \cr & \,\,\,\,\,\, = {{m\left[ {n - 4} \right] + 2n\left[ {n - 4} \right]} \over {m + 2n}}.{n \over {4 - n}} \cr & \,\,\,\,\, = {{\left[ {n - 4} \right]\left[ {m + 2n} \right].n} \over {\left[ {m + 2n} \right]\left[ {4 - n} \right]}} = {{ - \left[ {4 - n} \right]n} \over {4 - n}} = - n \cr & f]\,\,{{7{{\left[ {p - q} \right]}^2}} \over {pq}}.{{2{p^3}{q^2}} \over {p - {q^2}}} = {{7{{\left[ {p - q} \right]}^2}.2{p^3}{q^2}} \over {pq\left[ {p - {q^2}} \right]}} = {{14{{\left[ {p - q} \right]}^2}{p^2}q} \over {p - {q^2}}} \cr} \]