Bài 1: Thực hiện phép tính

a, \(\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}\)+\(\dfrac{2}{x^2+3}\)+\(\dfrac{1}{x+1}\)

b, \(\dfrac{x+y}{2\left(x-y\right)}\)-\(\dfrac{x-y}{2\left(x+y\right)}\)+\(\dfrac{2y^2}{x^2-y^2}\)

c, \(\dfrac{x-1}{x^3}\)-\(\dfrac{x+1}{x^3-x^2}\)+\(\dfrac{3}{x^3-2x^2+x}\)

d, \(\dfrac{xy}{ab}\)+\(\dfrac{\left(x-a\right)\left(y-a\right)}{a\left(a-b\right)}\)-\(\dfrac{\left(x-b\right)\left(y-b\right)}{b\left(a-b\right)}\)

e, \(\dfrac{x^3}{x-1}\)-\(\dfrac{x^2}{x+1}\)-\(\dfrac{1}{x-1}\)+\(\dfrac{1}{x+1}\)

f, \(\dfrac{x^3+x^2-2x-20}{x^2-4}\)-\(\dfrac{5}{x+2}\)+\(\dfrac{3}{x-2}\)

g, \(\left\{\dfrac{x-y}{x+y}+\dfrac{x+y}{x-y}\right\}\).\(\left\{\dfrac{x^2+y^2}{2xy}\right\}\).\(\dfrac{xy}{x^2+y^2}\)

h, \(\dfrac{1}{\left(a-b\right)\left(b-c\right)}\)+\(\dfrac{1}{\left(b-c\right)\left(c-a\right)}\)+\(\dfrac{1}{\left(c-a\right)\left(a-b\right)}\)

i, \(\dfrac{\left[a^2-\left(b+c\right)^2\right]\left(a+b-c\right)}{\left(a+b+c\right)\left(a^2+c^2-2ac-b^2\right)}\)

k, \(\left[\dfrac{x^2-y^2}{xy}-\dfrac{1}{x+y}\left\{\dfrac{x^2}{y}-\dfrac{y^2}{x}\right\}\right]\):\(\dfrac{x-y}{x}\)

Bài 2: Rút gọn các phân thức:

a, \(\dfrac{25x^2-20x+4}{25x^2-4}\)

b, \(\dfrac{5x^2+10xy+5y^2}{3x^3+3y^3}\)

c, \(\dfrac{x^2-1}{x^3-x^2-x+1}\)

d, \(\dfrac{x^3+x^2-4x-4}{x^4-16}\)

e, \(\dfrac{4x^4-20x^3+13x^2+30x+9}{\left(4x^2-1\right)^2}\)

Bài 3: Rút gọn rồi tính giá trị các biểu thức:

a, \(\dfrac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}\) với a = 4, b = -5, c = 6

b, \(\dfrac{16x^2-40xy}{8x^2-24xy}\) với \(\dfrac{x}{y}\) = \(\dfrac{10}{3}\)

c, \(\dfrac{\dfrac{x^2+xy+y^2}{x+y}-\dfrac{x^2-xy+y^2}{x-y}}{x-y-\dfrac{x^2}{x+y}}\) với x = 9, y = 10

Bài 4: Tìm các giá trị nguyên của biến số x để biểu thức đã cho cũng có giá trị nguyên:

a, \(\dfrac{x^3-x^2+2}{x-1}\)

b, \(\dfrac{x^3-2x^2+4}{x-2}\)

c, \(\dfrac{2x^3+x^2+2x+2}{2x+1}\)

d, \(\dfrac{3x^3-7x^2+11x-1}{3x-1}\)

e, \(\dfrac{x^4-16}{x^4-4x^3+8x^2-16x+16}\)

1. Cho a+b+c = 0. cmr ; \(a^3+b^3+a^2c+b^2c-abc=0\)
2. CMR: với mọi m thuộc Z

• \(m^3-m⋮6\)         
• \(m^3+5m⋮6\)
• \(m^3-19m⋮16\)
• \(\left(2m-1\right)^3-\left(2m-1\right)⋮8\)

      3. Tìm x, biết

• \(8x^3-50x=0\)
• \(\left(x-2\right)\left(x^2+2x+7\right)+2\left(x^2-4\right)-5\left(x-2\right)=0\)

      4. Tìm các cặp số nguyên x,y thỏa mãn

• \(y\left(x-2\right)+3x-6=2\)
• \(xy+3x-2y-7=0\)
• \(xy-x+5y-7=0\)

Bài 1: Phân tích đa thức thành nhân tử:

a) \(2x\left(x+1\right)+2\left(x+1\right)\)

b) \(y^2\left(x^2+y\right)-zx^2-zy\)

c) \(4x\left(x-2y\right)+8y\left(2y-x\right)\)

d) \(3x\left(x+1\right)^2-5x^2\left(x+1\right)+7\left(x+1\right)\)

e) \(x^2-6xy+9y^2\)

f) \(x^3+6x^2y+12xy^2+8y^3\)

g) \(x^3-64\)

h) \(125x^3+y^6\)

k) \(0,125\left(a+1\right)^3-1\)

t) \(x^2-2xy+y^2-xz+yz\)

q) \(x^2-y^2-x+y\)

p) \(a^3x-ab+b-x\)

đ) \(3x^2\left(a+b+c\right)+36xy\left(a+b+c\right)+108y^2\left(a+b+c\right)\)

l) \(x^2-x-6\)

i) \(x^4+4x^2-5\)

m) \(x^3-19x-30\)

j) \(x^4+x+1\)

y) \(ab\left(a-b\right)+bc\left(b-c\right)+ca\left(c-a\right)\)

o) \(\left(a+b+c\right)^3-a^3-b^3-c^3\)

ê) \(4a^2b^2-\left(a^2+b^2+c^2\right)^2\)

w) \(\left(1+x^2\right)^2-4x\left(1-x^2\right)\)

z) \(\left(x^2-8\right)^2+36\)

u) \(81x^4+4\)

Bài 2 : Tìm x

a)\(\left(2x-1\right)^2-25=0\)

b) \(8x^3-50x=0\)

c) \(\left(x-2\right)\left(x^2+2+7\right)+2\left(x^2-4\right)-5\left(x-2\right)=0\)

d) \(3x\left(x-1\right)+x-1=0\)

e) \(2\left(x+3\right)-x^2-3x\) =0

f) \(4x^2-25-\left(2x-5\right)\left(2x+7\right)=0\)

g) \(x^3+27+\left(x+3\right)\left(x-9\right)=0\)

Rút gọn biểu thức:

a) \(A=\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)

b) \(B=3x^2\left(x+1\right)\left(x-1\right)-\left(x^2-1\right)\left(x^4+x^2+1\right)+\left(x^2-1\right)^3\)

c) \(C=\left(x+y\right)\left(x^2-xy+y^2\right)+\left(x-y\right)\left(x^2+xy+y^2\right)-2x^3\)

d) \(D=\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)\)

Rút gọn biểu thức:

a) \(A=\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)

b) \(B=3x^2\left(x+1\right)\left(x-1\right)-\left(x^2-1\right)\left(x^4+x^2+1\right)+\left(x^2-1\right)^3\)

c) \(C=\left(x+y\right)\left(x^2-xy+y^2\right)+\left(x-y\right)\left(x^2+xy+y^2\right)-2x^3\)

d) \(D=\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)\)

 BÀI 1: Cho các đẳng thức sau: \(x+y=5\),  \(xy=1\)(điều kiện x+y+5 có thể thành \(x=5-y\)). Tính :

a)\(\left(x^2+\frac{1}{x}\right)\left(y^2+\frac{1}{y}\right)\)    c)\(x^3+x^4+y^3+y^4\)       e) \(\sqrt{x+1}+\sqrt{y+1}\)    g) \(\sqrt[x]{y}+\sqrt[y]{x}\)

b)\(x^3+y^3+\frac{1}{x}+\frac{1}{y}\)         d)\(x^2-y^2\)                       f) \(\sqrt[x]{x}+\sqrt[y]{y}\)                  h)\(x^5+y^5;x^6+y^6;x^7+y^7\)

BÀI 2: Cho x+y = m+1; xy = m-2

 a) tìm min A= \(x^2\left(y^2+1\right)+y^2\left(x^2=1\right)\)

b) tìm min B= \(1-x^2-y^2\)

c) tìm min C= \(\left(x+2y\right)\left(y+2x\right)\)

d) tìm min D= \(\left(x-3y\right)\left(y-3x\right)\)

nhanh tay

Phân tích các đa thức sau thành nhân tử:

* \(x^3-7x+6\)

* \(x^3-9x^2+6x+16\)

* \(x^3-6x^2-x+30\)

* \(2x^3-x^2+5x+3\)

* \(27x^3-27x^2+18x-4\)

* \(x^2+2xy+y^2-x-y-12\)

* \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

* \(4x^4-32x^2+1\)

* \(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\)

* \(64x^4+y^4\)

* \(a^6+a^4+a^2b^2+b^4-b^6\)

* \(x^3+3xy+y^3-1\)

* \(4x^4+4x^3+5x^2+2x+1\)

* \(x^8+x+1\)

* \(x^8+3x^4+4\)

* \(3x^2+22xy+11x+37y+7y^2+10\)

* \(x^4-8x+63\)

* \(\left(x+y+z\right)\left(xy+yz+zx\right)-xyz\)

* \(xy\left(x+y\right)-yz\left(y+z\right)+xz\left(x-z\right)\)

* \(\left(a+b\right)\left(a^2-b^2\right)+\left(b+c\right)\left(b^2-c^2\right)+\left(c+a\right)\left(c^2-a^2\right)\)

* \(a^4\left(b-c\right)+b^4\left(c-a\right)+c^4\left(a-b\right)\)

* \(a^3+b^3+c^3-3abc=\left(a+b\right)^3-3ab^2+c^3-3abc\)

* \(\left(a+b+c\right)^3-a^3-b^3-c^3=[\left(a+b\right)c]^3-a^3-b^3-c^3\)

* \(\left(x-y\right)^3+\left(y-z\right)^3+\left(z-x\right)^3\)

\([\) Các bạn làm được bài nài thì làm giúp mk với nha,làm vài câu cũng được\(]\)

Mk mệt quá rồi làm giúp mk với nha

Phân tích đa thức thành nhân tử

a, 5x-10\(x^2\)

b, \(\dfrac{1}{2}x\left(x^2-4\right)+4\left(y+2\right)\)

c, \(x^4-y^6\)

d, \(x^3+y\left(1-3x^2\right)+z\left(3y^2-1\right)-y^3\)

e, \(x^3-4x^2+4x-1\)

f, \(x^2+2xy-8y^2+2xz+14yz+3z^2\)

g, \(x^4+6x^3-12x^2-8x\)

h, \(\left(x^2+4x+8\right)^2+3x\left(x^2+4x+8\right)+2x^2\)