Đề kiểm tra 15 phút môn Toán Chương 2 Đại số 8: Rút gọn phân thức

Rút gọn phân thức:

a) \({{16{a^2} – 1} \over {16{a^2} – 8a + 1}}\)

b) \({{36a – {a^3}} \over {{a^3} + 12{a^2} + 36a}}\)

c) \({{2{a^4} + 3{a^3} + 2a + 3} \over {\left( {{a^2} – a + 1} \right)\left( {2a + 3} \right)}}.\)

a) \({{16{a^2} – 1} \over {16{a^2} – 8a + 1}} = {{\left( {4a – 1} \right)\left( {4a + 1} \right)} \over {{{\left( {4a – 1} \right)}^2}}} = {{4a + 1} \over {4a – 1}}.\)

b) \({{36a – {a^3}} \over {{a^3} + 12{a^2} + 36a}} = {{a\left( {36 – {a^2}} \right)} \over {a\left( {{a^2} + 12a + 36} \right)}}\)\(\; = {{a\left( {6 – a} \right)\left( {6 + a} \right)} \over {a{{\left( {a + 6} \right)}^2}}} = {{6 – a} \over {6 + a}}.\)

c) \({{2{a^4} + 3{a^3} + 2a + 3} \over {\left( {{a^2} – a + 1} \right)\left( {2a + 3} \right)}} = {{{a^3}\left( {2a + 3} \right) + \left( {2a + 3} \right)} \over {\left( {{a^2} – a + 1} \right)\left( {2a + 3} \right)}}\)\(\; = {{\left( {2a + 3} \right)\left( {{a^3} + 1} \right)} \over {\left( {{a^2} – a + 1} \right)\left( {2a + 3} \right)}}= {{\left( {a + 1} \right)\left( {{a^2} – a + 1} \right)} \over {{a^2} – a + 1}}\)\(\; = a + 1.\)