Giải các phương trình sau :
1.\(\dfrac{14}{3x-12}-\dfrac{2+x}{x-4}=\dfrac{3}{8-2x}-\dfrac{5}{6}\)
2.\(\dfrac{12}{1-9x^2}=\dfrac{1-3x}{1+3x}-\dfrac{1+3x}{1-3x}\)
3.\(\dfrac{x+5}{x^2-5x}-\dfrac{x+25}{2x^2-50}=\dfrac{x-5}{2x^2+10x}\)
4.\(\dfrac{6x_{ }+1}{x^2-7x+10}+\dfrac{5}{x-2}=\dfrac{3}{x-5}\)
5.\(\dfrac{2}{x^2-4}-\dfrac{x-1}{x\left(x-2\right)}+\dfrac{x-4}{x\left(x+2\right)}=0\)
6.\(\dfrac{2}{x+2}-\dfrac{2x^2+16}{x^3+8}=\dfrac{5}{x^2-2x+4}\)
a) \(\dfrac{1}{x^2+x}+\dfrac{1}{x^2+3x+2}+\dfrac{1}{x^2+5x+6}+\dfrac{1}{x^2+7x+12}\)
b) \(\dfrac{1}{x^2+3x+2}+\dfrac{1}{x^2+5x+6}+\dfrac{1}{x^2+7x+12}+\dfrac{1}{x^2+9x+20}\)
Rút gọn
A=\(\dfrac{\left(1^4+\dfrac{1}{4}\right)\left(3^4+\dfrac{1}{4}\right)\left(5^4+\dfrac{1}{4}\right)...\left(11^4+\dfrac{1}{4}\right)}{\left(2^4+\dfrac{1}{4}\right)\left(4^4+\dfrac{1}{4}\right)\left(6^4+\dfrac{1}{4}\right)...\left(12^4+\dfrac{1}{4}\right)}\)
1. Giải pt
b. x\(^3\)-16x\(^2\)+64x= 0
c.|6x-1|= 2x+5
d. |5-x|= 8x-10
e. \(\dfrac{x-1}{x+3}\)= \(\dfrac{x}{x-3}\)+ \(\dfrac{12}{x^2-9}\)
g. \(\dfrac{x+2}{x-2}\)- \(\dfrac{x-2}{x+2}\)= \(\dfrac{6}{x^2-4}\)
CMR \(\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{1}{x\left(x+1\right)}\)
áp dụng kết quả bài toán trên, tính:
\(\dfrac{1}{^{^{ }}x^2+x}+\dfrac{1}{x^2+3\text{x}+2}+\dfrac{1}{x^2+6\text{x}+6}+\dfrac{1}{x^2+7\text{x}+12}+\dfrac{1}{x^2+9\text{x}+20}+\dfrac{1}{x+5}_{ }\)
Bài 1: Rút gọn phân thức
a) \(\dfrac{36\left(x-2\right)^3}{32-16x}\)
b) \(\dfrac{x^2+2x+1}{x+1}\)
c) \(\dfrac{x^2-2x+1}{x^2-1}\)
d) \(\dfrac{3x^2-12x+12}{x^4-8x}\)
2. Giải Bpt, biểu diễn tập nghiệm
a. -12x+1> 13
b. \(\dfrac{3x-1}{3}\)-12\(\ge\) x+ \(\dfrac{6x+1}{7}\)
c. \(\dfrac{5+3x}{4}\)- 2x \(\le\) 4+ \(\dfrac{x+8}{3}\)
Thực hiện phép tính sau:
a, (6x3y2 - 4x2y3 - 10x2y2) : 2xy
b, \(\dfrac{2y}{x-2}\) + \(\dfrac{5y}{x-2}\)
c, \(\dfrac{xy}{3x-y}\) + \(\dfrac{3x^2}{y-3x}\)
d, \(\dfrac{x-1}{6x+12}\) . \(\dfrac{x+2}{x-1}\)
Tìm x
\(\dfrac{x+1}{3}\)+\(\dfrac{3.\left(2x+1\right)}{4}\)=\(\dfrac{2x+3.\left(x+1\right)}{6}\)+\(\dfrac{7+12x}{12}\)
