Đề bài

Thực hiện phân thức:

a) \({5 \over {3x}} - {2 \over {3x}}\) ;

b) \({{ - 5} \over {7y}} - {6 \over {7y}}\) ;

c) \({{7x} \over {x - y}} - {{2x + 3} \over {x - y}}\) ;

d) \({1 \over {3c}} - {1 \over {3d}}\) ;

e) \({{f - 4h} \over {3k}} - {{2f - 5h} \over {8k}}\) ;

f) \({{p + 3} \over {2z}} + {{p - 1} \over {6z}} - {{2p + 1} \over {3z}}\) .

Lời giải chi tiết

\(\eqalign{  & a)\,\,{5 \over {3x}} - {2 \over {3x}} = {{5 - 2} \over {3x}} = {3 \over {3x}} = {1 \over x}  \cr  & b)\,\,{{ - 5} \over {7y}} - {6 \over {7y}} = {{ - 5} \over {7y}} + {{ - 6} \over {7y}} = {{ - 5 - 6} \over {7y}} = {{ - 11} \over {7y}}  \cr  & c)\,\,{{7x} \over {x - y}} - {{2x + 3} \over {x - y}} = {{7x} \over {x - y}} + {{ - \left( {2x + 3} \right)} \over {x - y}}  \cr  & \,\,\,\,\, = {{7x - 2x - 3} \over {x - y}} = {{5x - 3} \over {x - y}}  \cr  & d)\,\,{1 \over {3c}} - {1 \over {3d}} = {1 \over {3c}} + {{ - 1} \over {3d}}  \cr  & \,\,\,\,\, = {{1.d} \over {3c.d}} + {{ - 1.c} \over {3d.c}} = {{d - c} \over {3cd}}  \cr  & e)\,\,{{f - 4h} \over {3k}} - {{2f - 5h} \over {8k}} = {{f - 4h} \over {3k}} + {{ - \left( {2f - 5h} \right)} \over {8k}}  \cr  & \,\,\,\,\, = {{\left( {f - 4h} \right).8} \over {3k.8}} + {{ - \left( {2f - 5h} \right).3} \over {8k.3}}  \cr  & \,\,\,\,\, - {{8f - 32h - 6f + 15h} \over {24k}} = {{2f - 32k + 15h} \over {24k}}  \cr  & f)\,\,{{p + 3} \over {2z}} + {{p - 1} \over {6z}} - {{2p + 1} \over {3z}}  \cr  & \,\,\,\,\, = {{\left( {p + 3} \right).3} \over {2z.3}} + {{p - 1} \over {6z}} - {{\left( {2p + 1} \right).2} \over {3z.2}}  \cr  & \,\,\,\,\, = {{3p + 9 + p - 1 - 4p - 2} \over {6z}} = {6 \over {6z}} = {1 \over z} \cr} \)

dapandethi.vn