Câu 1: Giải PT:

a) 2x² - 6x + 1 = 0

b) x³ + x = 2

c) (x-2)(x+1) < 0

d) \(\dfrac{2x-5}{x+5}\) > 0

Câu 2: Chứng minh bất đẳng thức sau:

a) 2x - x² \(\le\) 1 với mọi x

b) A = (a+b)\(\left(\dfrac{1}{a}+\dfrac{1}{b}\right)\)\(\ge\) 4

c) B = \(\dfrac{a+b}{c}+\dfrac{b+a}{a}+\dfrac{c+a}{b}\ge6\) (a,b,c > 0)

d) \(\dfrac{a}{4b^2+1}+\dfrac{b}{4a^2+1}\ge\dfrac{1}{2}\) (a,b dương; a+b=4ab)

Giải các bất đẳng thức:

a. \(\dfrac{5\left(x-1\right)}{6}\)-1≥ \(\dfrac{2\left(x+1\right)}{3}\)

b. \(\dfrac{x+7}{15}\)> \(\dfrac{2x}{5}\)-\(\dfrac{x}{3}\)+\(\dfrac{7}{15}\)

c. 8x-3< 5(\(\dfrac{8x}{5}\)+3)

d.\(\dfrac{3x+5}{2}\)-1≤\(\dfrac{x+2}{3}\)+x

a) \(\dfrac{4x-8}{2x+1}\)=0 b) 2-\(\dfrac{x}{x-2}\)=\(\dfrac{x+1}{x+2}\) c)\(\dfrac{x+2}{x-3}\)=\(\dfrac{x}{x+1}\) d) \(\dfrac{3}{x-2}\)=\(\dfrac{1}{x}\) e) \(\dfrac{x-2}{x}\)=\(\dfrac{x-3}{x+2}\) f) \(\dfrac{2x}{x+1}\)-\(\dfrac{1}{x-2}\)=\(\dfrac{2x^2-16}{\left(x+1\right)\left(x-2\right)}\) g) \(\dfrac{3x}{x-1}+\dfrac{2}{x+1}=\dfrac{3x^2}{\left(x-1\right)\left(x+1\right)}\) h) \(\dfrac{1-x}{4}=\dfrac{2x+1}{5}\) i)\(\dfrac{2-3x}{3}=\dfrac{x+4}{4}\) m) \(\dfrac{4x+3}{5}=\dfrac{3-4x}{3}\) n) \(\dfrac{7-3x}{4}-2=\dfrac{x+5}{3}\)

Giải các phương trình có chứa ẩn ở mẫu sau:

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

b, \(\left(x-2\right)\left(\dfrac{2}{3}x-6\right)=0\)

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

f, \(\dfrac{x-1}{x}+\dfrac{x-2}{x+1}=2\)

g, \(\dfrac{x}{x-1}+\dfrac{x-1}{x}=2\)

h, \(\dfrac{x+3}{x+1}+\dfrac{x-2}{x}=2\)

i, \(\dfrac{2}{x+1}-\dfrac{3}{x-1}=5\)

j, \(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}=\dfrac{8}{4x^2-1}\)

k, \(\dfrac{3x-1}{x-1}-\dfrac{2x+5}{x-3}=1\)

l, \(\dfrac{2}{x+1}-\dfrac{1}{xx-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

m, \(\dfrac{3x-1}{x-1}-\dfrac{2x+5}{x+3}+\dfrac{4}{x^2+2x-3}=1\)

n, \(\dfrac{x+2}{x-2}-\dfrac{1}{x}=\dfrac{2}{x\left(x-2\right)}\)

o, \(\dfrac{x-2}{x+2}+\dfrac{3}{x-2}=\dfrac{x^2-11}{x^2-4}\)

p, \(\dfrac{x+4}{x+1}+\dfrac{x}{x-1}=\dfrac{2x^2}{x^2-1}\)

z, \(\dfrac{2x}{x-1}+\dfrac{4}{x^2+2x-3}=\dfrac{2x-5}{x+3}\)

q, \(\dfrac{x^2-x}{x+3}-\dfrac{x^2}{x-3}=\dfrac{7x^2-3x}{9-x^2}\)

r, \(\dfrac{1}{x-3}+2=\dfrac{5}{x-1}+x\)

s, \(\dfrac{2}{x^2+4x-21}=\dfrac{3}{x-3}\)

Làm tính trừ phân thức :

a) \(\dfrac{3x-2}{2xy}-\dfrac{7x-4}{2xy}\)

b) \(\dfrac{3x+5}{4x^3y}-\dfrac{5-15x}{4x^3y}\)

c) \(\dfrac{4x+7}{2x+2}-\dfrac{3x+6}{2x+2}\)

d) \(\dfrac{9x+5}{2\left(x-1\right)\left(x+3\right)^2}-\dfrac{5x-7}{2\left(x-1\right)\left(x+3\right)^2}\)

e) \(\dfrac{xy}{x^2-y^2}-\dfrac{x^2}{y^2-x^2}\)

f) \(\dfrac{5x+y^2}{x^2y}-\dfrac{5y-x^2}{xy^2}\)

g)\(\dfrac{x}{5x+5}-\dfrac{x}{10x-10}\)

h) \(\dfrac{x+9}{x^2-9}-\dfrac{3}{x^2+3x}\)

4.Giải phương trình

a) \(\dfrac{x+5}{x-5}-\dfrac{x-5}{x+5}=\dfrac{20}{x^2-25}\)

b)\(\dfrac{1}{x-1}+\dfrac{2}{x+1}=\dfrac{x}{x^2-1}\)

c)\(5+\dfrac{76}{x^2-16}=\dfrac{2x-1}{x+4}-\dfrac{3x-1}{4-x}\)

d)\(\dfrac{90}{x}-\dfrac{36}{x-6}=2\)

e)\(\dfrac{1}{x}+\dfrac{1}{x+10}=\dfrac{1}{12}\)

f)\(\dfrac{x+3}{x-3}-\dfrac{1}{x}=\dfrac{3}{x\left(x-3\right)}\)

g)\(\dfrac{3}{x+2}-\dfrac{2}{x-2}+\dfrac{8}{x^2-4}=0\)

h)\(\dfrac{3}{x+2}-\dfrac{2}{x-3}=\dfrac{8}{\left(x-3\right)\left(x+2\right)}\)

i)\(\dfrac{x}{2x+6}-\dfrac{x}{2x+2}=\dfrac{3x+2}{\left(x+1\right)\left(x+3\right)}\)

k)\(\dfrac{x}{x+1}-\dfrac{2x-3}{1-x}=\dfrac{3x^2+5}{x^2-1}\)

l)\(\dfrac{5}{x+7}+\dfrac{8}{2x+14}=\dfrac{3}{2}\)

m)\(\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x^2+x}\)

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