\(\frac{\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+4}{x^2+5x+4}\)
\(=\frac{\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+4}{x^2+x+4x+4}\)
\(=\frac{\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+4}{x\left(x+1\right)+4\left(x+1\right)}\)
\(=\frac{\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+4}{\left(x+1\right)\left(x+4\right)}\)
\(=\left(x+2\right)\left(x+3\right)+4\)
Rút gọn và tính giá trị của biểu thức
a) \(4x^2\left(5x-3y\right)-5x^2\left(4x+y\right)vớix=-2,y=-3\)
b)\(\left(x-4\right)\left(x-2\right)-\left(x-1\right)\left(x-3\right)vớix=\frac{7}{4}\)
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
\(\dfrac{\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1}{x^2+5x+5}\)
\(\left(\frac{x+2}{2-x}-\frac{2-x}{x+2}-\frac{4x^2}{x^2-4}\right):\left(\frac{x^2-6x+9}{\left(2-x\right).\left(x-3\right)}\right)\)
Rút gọn phân thức:
1, \(\dfrac{x^2+y^2-1+2xy}{x^2-y^2+1+2x}\)
2, \(\dfrac{x^4-y^4}{x^3+y^3}\)
3, \(\dfrac{x^3+y^3+z^3-3xyz}{\left(x-y\right)^2+\left(x-z\right)^2+\left(y-z\right)^2}\)
4, \(\dfrac{\left(x^2-y^2\right)^3+\left(y^2-z^2\right)^3+\left(z^2-x^2\right)^3}{\left(x-y\right)^3+\left(y-z\right)^3+\left(z-x\right)^3}\)
5, \(\dfrac{x^3-7x+6}{x^2\left(x-3\right)^2+4x\left(3-x\right)^2+4\left(x-3\right)^2}\)
Rút gọn các phân thức :
a) \(\dfrac{14xy^5\left(2x-3y\right)}{21x^2y\left(2x-3y\right)^2}\)
b) \(\dfrac{8xy\left(3x-1\right)^3}{12x^3\left(1-3x\right)}\)
c) \(\dfrac{20x^2-45}{\left(2x+3\right)^2}\)
d) \(\dfrac{5x^2-10xy}{2\left(2y-x\right)^3}\)
e) \(\dfrac{32x-8x^2+2x^3}{x^3+64}\)
f) \(\dfrac{9-\left(x+5\right)^2}{x^2+4x+4}\)
g) \(\dfrac{80x^3-125x}{3\left(x-3\right)-\left(x-3\right)\left(8-4x\right)}\)
h) \(\dfrac{5x^3+5x}{x^4-1}\)
i) \(\dfrac{x^2+5x+6}{x^2+4x+4}\)
Bài 9. Rút gọn các phân thức sau
a) \(\frac{a^3+b^3+c^3-3abc}{a^2+b^2+c^2-ab-bc-ca}\)
d) \(\frac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{a^4\left(b^2-c^2\right)+b^4\left(c^2-a^2\right)+c^4\left(a^2-b^2\right)}\)
e) \(\frac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{ab^2-ac^2-b^3+bc^2}\)
f) \(\frac{x^{24}+x^{20}+x^{16}+...+x^4+1}{x^{26}+x^{24}+x^{22}+...+x^2+1}\)
1. Tìm giá trị của x để các phân thức sau = 0 .
a) \(\dfrac{x^4+x^3+x+1}{x^4-x^3+2x^2-x+1}\)
b)\(\dfrac{x^4-5x^2+4}{x^4-10x^2+9}\)
2. Rút gọn các phân thức :
a) \(\dfrac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{ab^2-ac^2-b^3+bc^2}\)
b) \(\dfrac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}\)
c) \(\dfrac{x^3-y^3+z^3+3xyz}{\left(x+y\right)^2+\left(y+x\right)^2+\left(z-x\right)^2}\)
d)\(\dfrac{x^3+y^3+z^3-3xyz}{\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2}\)
\(\dfrac{\text{80x3-125x}}{3\left(x-3\right)-\left(x-3\right)\left(8-4x\right)}\) \(\dfrac{9-\left(x+5^{ }\right)^2}{x^2+4x+4}\)
\(\dfrac{32x-8x^2+2x^3}{x^3+64}\) \(\dfrac{x^2+5x+6}{x^2+4x+4}\)