(2đ) Rút gọn các phân thức sau:a)...

- Hướng dẫn giải

Phương pháp giải:

Giải chi tiết:

Hướng dẫn giải chi tiết:

a)      \(\dfrac{{5(x - y) - 3(y - x)}}{{10(x - y)}} = \dfrac{{5(x - y) + 3(x - y)}}{{10(x - y)}} = \dfrac{{8(x - y)}}{{10(x - y)}} = \dfrac{4}{5}\)

b)      \(\dfrac{{{x^2} + 4x + 3}}{{2x + 6}} = \dfrac{{{x^2} + x + 3x + 3}}{{2(x + 3)}} = \dfrac{{x(x + 1) + 3(x + 1)}}{{2(x + 3)}} = \dfrac{{(x + 1)(x + 3)}}{{2(x + 3)}} = \dfrac{{x + 1}}{2}\) .

c)      \(\dfrac{{{y^2} - {x^2}}}{{{x^2} - 3xy + 2{y^2}}} = \dfrac{{(y - x)(y + x)}}{{{x^2} - xy - 2xy + 2{y^2}}} = \dfrac{{(x + y)(y - x)}}{{x(x - y) - 2y(x - y)}} = \dfrac{{ - (x + y)(x - y)}}{{(x - y)(x - 2y)}} = \dfrac{{ - (x + y)}}{{x - 2y}}.\)

d)      \(\dfrac{{2{x^3} - 7{x^2} - 12x + 45}}{{3{x^3} - 19{x^2} + 33x - 9}} = \dfrac{{2{x^3} + 5{x^2} - 12{x^2} - 30x + 18x + 45}}{{3{x^3} - {x^2} - 18{x^2} + 6x + 27x - 9}} = \dfrac{{{x^2}(2x + 5) - 6x(2x + 5) + 9(2x + 5)}}{{{x^2}(3x - 1) - 6x(3x - 1) + 9(3x - 1)}}\)

 \( = \dfrac{{(2x + 5)({x^2} - 6x + 9)}}{{(3x - 1)({x^2} - 6x + 9)}} = \dfrac{{2x + 5}}{{3x - 1}}.\)