\(=\dfrac{x^2-x+1-3+3x+3}{\left(x+1\right)\left(x^2-x+1\right)}\cdot\dfrac{3\left(x^2-x+1\right)}{\left(x+1\right)\left(x+2\right)}-\dfrac{2x-2}{x\left(x+2\right)}\)
\(=\dfrac{x^2+2x+1}{x+1}\cdot\dfrac{3}{\left(x+1\right)\left(x+2\right)}-\dfrac{2x-2}{x\left(x+2\right)}\)
\(=\dfrac{3}{x+2}-\dfrac{2x-2}{x\left(x+2\right)}=\dfrac{3x-2x+2}{x\left(x+2\right)}=\dfrac{1}{x}\)
Tìm x :
a, \(\left(2x+1\right)^2-3x^2+4=\left(1-x\right).\left(1+x\right)\)
b, \(\left(4x-3\right)\cdot\left(4x+3\right)-2\cdot\left(x+2\right)^2=14x^2\)
c, \(\left(2x-1\right)\cdot\left(x+1\right)-x^2+1=\dfrac{1}{2}\cdot\left(x-1\right)^2\)
giải pt
a.\(\dfrac{3x-1}{x-1}-\dfrac{2x+5}{x+3}=1-\dfrac{4}{\left(x-1\right)\left(x+3\right)}\)
b. \(\dfrac{13}{\left(x-3\right)\left(2x+7\right)}+\dfrac{1}{2x+7}=\dfrac{6}{\left(x-3\right)\left(x+3\right)}\)
giải pt sau
g) 11+8x-3=5x-3+x
h)4-2x+15=9x+4-2x
g)\(\dfrac{3x+2}{2}-\dfrac{3x+1}{6}=\dfrac{5}{3}+2x\)
h)\(\dfrac{x+4}{5}-x+4=\dfrac{4x+2}{5}-5\)
i)\(\dfrac{4x+3}{5}-\dfrac{6x-2}{7}=\dfrac{5x+4}{3}+3\)
k) \(\dfrac{5x+2}{6}-\dfrac{8x-1}{3}=\dfrac{4x+2}{5}-5\)
m) \(\dfrac{2x-1}{5}-\dfrac{x-2}{3}=\dfrac{xx+7}{15}\)
n)\(\dfrac{1}{4}\left(x+3\right)=3-\dfrac{1}{2}\left(x+1\right)-\dfrac{1}{3}\left(x+2\right)\)
p)\(\dfrac{x}{3}-\dfrac{2x+1}{6}=\dfrac{x}{6}-x\)
q)\(\dfrac{2+x}{5}-0,5x=\dfrac{1-2x}{4}+0,25\)
1. làm tính nhân
a,\(2x.\left(x^2-7x-3\right)\)
b,\(\left(-2x^3+\dfrac{3}{4}y^2-7xy\right).4xy^2\)
c,\(\left(-5x^3\right).\left(2x^2+3x-5\right)\)
d,\(\left(2x^2-\dfrac{1}{3}xy+y^2\right).\left(-3x^3\right)\)
e,\(\left(x^2-2x+3\right).\left(x-4\right)\)
f,\(\left(2x^3-3x-1\right).\left(5x+2\right)\)
2.tính nhanh
a,\(892^2+892.216+108^2\)
b,\(36^2+26^2-52.36\)
3.tìm x biết
a,\(7x^2-28=0\)
b,\(\dfrac{2}{3}x.\left(x^2-4\right)=0\)
c,\(2x.\left(3x-5\right)-\left(5-3x\right)=0\)
d,\(\left(2x-1\right)^2-25=0\)
4.rút gọn và tính gái trị biểu thức
M=\(\left(x+3\right)\left(x^2-3x+9\right)-\left(x^3+54-x\right)\)
với x=27
Câu 1 : Cho biểu thức \(A=\left(\dfrac{x^2-2x}{2x^2+8}-\dfrac{2x^2}{8-4x+2x^2-x^3}\right)\left(1-\dfrac{1}{x}-\dfrac{2}{x^2}\right)\)
a) Tìm ĐKXĐ và rút gọn biểu thức A
b) Tìm số nguyên x để A nhận giá trị là một số nguyên
Chứng minh biểu thức không phụ thuộc x :
1, \(\left(3x-1\right)^2-2\cdot\left(2x-3\right)\cdot\left(2x+3\right)-\left(x-3\right)^2\)
2, \(\left(3x+2\right)^3-\left(3x-2\right)^3-3\cdot\left(6x-1\right)\cdot\left(6x+1\right)\)
3, \(\left(3x-5\right)^2+3\cdot\left(x+1\right)\cdot\left(x-1\right)-\left(4x-3\right)^2+\left(2x+2\right)\cdot\left(2x+1\right)\)
1. tính
a) \(\left(\dfrac{2}{3}x-\dfrac{3}{2}y\right)^2\)
b) \(\left(\dfrac{1}{2}x^2+\dfrac{1}{3}\right)^2\)
c) \(\left(x+\dfrac{1}{5}y^2\right)\left(x-\dfrac{1}{5}y^2\right)\)
d) \(\left(\dfrac{1}{2}x-2y\right)^3\)
e) \(\left(-\dfrac{1}{2}xy^2+x\right)^3\)
f) \(27x^3-8y^3\)
g) 4(2x - 3y) - 4 - (2x-3y)2
2. rút gọn
a) \(2m\left(5m+2\right)+\left(2m-3\right)\left(3m-1\right)\)
b) \(\left(2x+4\right)\left(8x-3\right)-\left(4x+1\right)^2\)
c) \(\left(7y-2\right)^2-\left(7y+1\right)\left(7y-1\right)\)
d) \(\left(a+2\right)^3-a\left(a-3\right)^2\)
3. c/m các biểu thức sau ko phụ thuộc vào biến x,y
a) \(\left(2x-5\right)\left(2x+5\right)-\left(2x-3\right)^2-12x\)
b) \(\left(2y-1\right)^3-2y\left(2y-3\right)^2-6y\left(2y-2\right)\)
c) \(\left(x+3\right)\left(x^2-3x+9\right)-\left(20+x^3\right)\)
d) \(3y\left(-3y-2\right)^2-\left(3y-1\right)\left(9y^2+3y+1\right)-\left(-6y-1\right)^2\)
4. Tìm x
a) \(\left(2x+5\right)\left(2x-7\right)-\left(-4x-3\right)^2=16\)
b) \(\left(8x^2+3\right)\left(8x^2-3\right)-\left(8x^2-1\right)^2=22\)
c) \(49x^2+14x+1=0\)
d) \(\left(x-1\right)^3-x\left(x-2\right)^2-\left(x-2\right)=0\)
5. c/m biểu thức luôn dương:
a) \(A=16x^2+8x+3\)
b) \(B=y^2-5y+8\)
c) C= \(2x^2-2x+2\)
d) \(D=9x^2-6x+25y^2+10y+4\)
6. Tìm GTLN và GTNN của các biểu thức sau
a) \(M=x^2+6x-1\)
b) \(N=10y-5y^2-3\)
7. thu gọn
a) \(\left(2+1\right)\left(2^2+1\right)\left(2^3+1\right)...\left(2^{32}+1\right)-2^{64}\)
b) \(\left(5+3\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{\text{64}}+3^{64}\right)+\dfrac{5^{128}-3^{128}}{2}\)
a. \(\dfrac{x-1}{x^{2^{ }}-4}=\dfrac{3}{2-x}\)
b. \(\dfrac{1}{x-1}-\dfrac{7}{x-2}=\dfrac{1}{\left(x-1\right)\left(2-x\right)}\)
c. \(\dfrac{2x+3}{2x-3}-\dfrac{3}{4x-6}=\dfrac{2}{5}\)
d. \(\dfrac{x+29}{31}-\dfrac{x+27}{33}=\dfrac{x+17}{43}-\dfrac{x+15}{45}\)
Chứng minh giá trị biểu thức không phụ thuộc x :
1, \(\left(2x+1\right)^3-\left(2x-1\right)^3-2\cdot\left(4x+3\right)^2+8\cdot\left(x+3\right)^2\)
2,\(\left(2x+1\right)^2\cdot\left(x-1\right)-2\cdot\left(x-2\right)^3+x\cdot\left(3-2x\right)\cdot\left(3+x\right)-\left(3x-3\right)^2\)
