\(\dfrac{27a^3+b^3}{3ab+b^2}\\ =\dfrac{\left(3a+b\right)\left(9a^2-3ab+b^2\right)}{b\left(3a+b\right)}\\ =\dfrac{9a^2-3ab+b^2}{b}\)
\(=\dfrac{\left(3a+b\right)\left(9a^2-3ab+b^2\right)}{b\left(3a+b\right)}=\dfrac{9a^2-3ab+b^2}{b}\)
\(\dfrac{27a^3+b^3}{3ab+b^2}\\ =\dfrac{\left(3a+b\right)\left(9a^2-3ab+b^2\right)}{b\left(3a+b\right)}\\ =\dfrac{9a^2-3ab+b^2}{b}\)
\(=\dfrac{\left(3a+b\right)\left(9a^2-3ab+b^2\right)}{b\left(3a+b\right)}=\dfrac{9a^2-3ab+b^2}{b}\)
bài 1 : Rút gọn
8) x+3/x^2-3x
9) x-2/x-5÷(x-2)^2/x^2-25
10) 1÷(1-1/a)
11) (a+6/3a+9-1/a+3)÷a+2/27a
12) 6x+6/3x^2+3x
13) 3/x+3 -x-6/x^2+3x
14) (x/x+2+2/x-2+4x/x^2-4)×x^2-2x+4/x+2
1/cho a + b + c = 0. Rút gọn biểu thức:
\(B=\dfrac{a^2}{a^2-b^2-c^2}+\dfrac{b^2}{b^2-c^2-a^2}+\dfrac{c^2}{c^2-b^2-a^2}\)
2/ cho \(P=\dfrac{a^3}{a^2+ab+b^2}+\dfrac{b^3}{b^2+bc+c^2}+\dfrac{c^3}{c^2+ca+a^2}\\ Q=\dfrac{b^3}{a^2+ab+b^2}+\dfrac{c^3}{b^2+bc+c^2}+\dfrac{a^3}{c^2+ca+a^2}\)
CMR: P = Q
\(a,\dfrac{a^3+b^3+c^3-3abc}{a^2+b^2+c^2-ab-bc-ca}\) \(d,\dfrac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{a^4\left(b^2-c^2\right)+b^4\left(c^2-a^2\right)+c^4\left(a^2-b^2\right)}\)
\(b,\dfrac{x^3-y^3+z^3+3xyz}{\left(x+y\right)^2+\left(y+z\right)^2+\left(z-x\right)^2}\) \(e,\dfrac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{ab^2-ac^2-b^3+bc^2}\)
\(c,\dfrac{x^3+y^3+z^3-3xyz}{\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2}\)
Rút gọn phân thức:
a, \(\dfrac{x^3-x^2y+xy^2-y^3}{x^2y+xy^2-x^3-y^3}\)
b, \(\dfrac{a^3+b^3+c^3-3abc}{\left(a-b\right)^3+\left(b-c\right)^3+\left(c-a\right)^3}\) biết a+b+c = 3
rút gọn ptđs
\(\dfrac{a^3\left(b^2-c^2\right)+b^3\left(c^2-a^2\right)+c^3\left(a^2-b^2\right)}{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}\)
\(\dfrac{\left(a-b\right)^3+\left(b-c\right)^3+\left(a-c\right)^3}{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}\)
Rút gọn phân thức
1/\(\frac{x^{3^{ }}-y^{3^{ }}+z^{3^{ }}+3xyz}{\left(x+y\right)^{2^{ }}+\left(y+z\right)^2+\left(z-x\right)^2}\)
2/\(\frac{x^{3^{ }}+y^{3^{ }}+z^3-3xyz}{\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2}\)
3/\(\frac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{a^4\left(b^2-c^2\right)+b^4\left(c^2-a^3\right)+c^4\left(a^2-b^2\right)}\)
Rút gọn các phân thức :
\(A=\dfrac{x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)}{xy^2-xz^2-y^3+yz^2}\)
\(B=\dfrac{a^3-b^3+c^3+3abc}{\left(a+b\right)^2+\left(b-c\right)^2+\left(c+a\right)^2}\)
\(C=\dfrac{a^3b-ab^3+b^3c-bc^3+c^3a-ca^3}{a^2b-ab^2+b^2c-bc^2+c^2a-ca^2}\)
bài 1 rút gọn
A=(x-1)2 + (x+3)(x-2)-2x2 +8
B=(2x -5 )(2x+5)-(2x+3)2 - 6x+2
C=(x+2)3 - (x-3)(x2+3x+9)-8x2 +6x-2020
D=(a+b+c)2-(a+b-c)2+(a-b-c)2
E=(a+1)2+(b+1)2+(c+1)2+2(ab+bc+ca)-(a+b+c+1)2
các bạn trình bày rõ giúp mình với nha
\(\dfrac{\left(a-b\right)^3-\left(b-c\right)^3-\left(a-c\right)^3}{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}\)
Rút gọn biểu thức trên