Question

Rút gọn các phân thức sau :

a) \(\dfrac{\left(a+b\right)^2-c}{a+b+c}\)

b) \(\dfrac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}\)

c)\(\dfrac{2x^2-7x^2-12x+45}{3x^3-19x^3+33x-9}\)

Answer 1

a) sai đề

b) \(\dfrac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}=\dfrac{\left(a^2+2ab+b^2\right)-c^2}{\left(a^2+2ac+c^2\right)-b^2}=\dfrac{\left(a+b\right)^2-c^2}{\left(a+c\right)^2-b^2}=\dfrac{\left(a+b-c\right)\left(a+b+c\right)}{\left(a+c-b\right)\left(a+c+b\right)}=\dfrac{a+b-c}{a-b+c}\)

c) xem lại đề có j ib lại tui

Answer 2

a: Sửa đề: \(\dfrac{\left(a+b\right)^2-c^2}{a+b+c}\)

\(=\dfrac{\left(a+b+c\right)\left(a+b-c\right)}{a+b+c}=a+b-c\)

c: Sửa đề: \(\dfrac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}\)

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

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