Đề bài
Thực hiện các phép chia phân thức:
a] \[{{a - 2b} \over {16}}:{{2a - 4b} \over {12}}\] ;
b] \[{{3[c + d]} \over {c - d}}:{{12c + 12d} \over {3c - 3d}}\] ;
c] \[{{a - 2b} \over 8}:{{4a - 8b} \over {12}}\] ;
d] \[{{8{c^3}} \over {6[c + d]}}:{{2{c^2}} \over {3c + 3d}}\] .
Lời giải chi tiết
\[\eqalign{ & a]\,\,{{a - 2b} \over {16}}:{{2a - 4b} \over {12}} = {{a - 2b} \over {16}}.{{12} \over {2a - 4b}} = {{\left[ {a - 2b} \right].12} \over {16\left[ {2a - 4b} \right]}} \cr & = {{\left[ {a - 2b} \right].12} \over {32\left[ {a - 2b} \right]}} = {3 \over 8} \cr & b]\,\,{{3\left[ {c + d} \right]} \over {c - d}}:{{12c + 12d} \over {3c - 3d}} = {{3\left[ {c + d} \right]} \over {c - d}}.{{3c - 3d} \over {12c + 12d}} \cr & = {{3\left[ {c + d} \right]\left[ {3c - 3d} \right]} \over {\left[ {c - d} \right]\left[ {12c + 12d} \right]}} = {{3\left[ {c + d} \right]3\left[ {c - d} \right]} \over {\left[ {c - d} \right]12\left[ {c + d} \right]}} = {3 \over 4} \cr & c]\,\,{{a - 2b} \over 8}:{{4a - 8b} \over {12}} = {{a - 2b} \over 8}.{{12} \over {4a - 8b}} \cr & = {{\left[ {a - 2b} \right].12} \over {8\left[ {4a - 8b} \right]}} = {{\left[ {a - 2b} \right].12} \over {32\left[ {a - 2b} \right]}} = {3 \over 8} \cr & d]\,\,{{8{c^3}} \over {6\left[ {c + d} \right]}}:{{2{c^2}} \over {3c + 3d}} = {{8{c^3}} \over {6\left[ {c + d} \right]}}.{{3c + 3d} \over {2{c^2}}} \cr & = {{8{c^3}.\left[ {3c + 3d} \right]} \over {6\left[ {c + d} \right].2{c^2}}} = {{8{c^3}.3\left[ {c + d} \right]} \over {6\left[ {c + d} \right].2{c^2}}} = {3 \over 4} \cr} \]