\(=\left(\dfrac{2}{2a-b}-\dfrac{6b}{\left(2a-b\right)\left(2a+b\right)}-\dfrac{4}{2a+b}\right):\dfrac{4a^2-b^2+4a^2+b^2}{4a^2-b^2}\)
\(=\dfrac{4a+2b-6b-8a+4b}{\left(2a-b\right)\left(2a+b\right)}\cdot\dfrac{\left(2a-b\right)\left(2a+b\right)}{8a^2}\)
\(=\dfrac{-4a}{8a^2}=\dfrac{-1}{2a}\)
Chứng minh biểu thức không phụ thuộc vào biến
A= (\(\dfrac{2}{2a-b}\)+\(\dfrac{6b}{b^{2^{ }}-4a^2}\)-\(\dfrac{4}{2a+b}\)):(1+\(\dfrac{4a^{2^{ }}+b^2}{4a^2-b^2}\))
Giải phương trình:
a, \(\dfrac{t}{2a}-\dfrac{4a}{3}=1\)
b, \(\dfrac{x-2a}{b}=2+\dfrac{x+b}{a}\) (a, b là các hằng số)
Câu 1: giải và biện luận phương trình theo tham số a và b:
(ab + 2) x - 2b = (b + 2a) x - a
Câu 2: giải và biện luận phương trình theo tham số a:
a) a3x - 16a (x + 1) = 4a2 + 16
b) m2x - m + 3mx = 4x - 1
c)\(\dfrac{x-4a}{a+1}+\dfrac{4-x}{1-a}=\dfrac{4a+3-x}{1-a^2}\)
giải các phương trình ẩn x sau:
a) \(\dfrac{1}{3x}\)+\(\dfrac{1}{2x}\)=\(\dfrac{1}{4}\)
b) \(\dfrac{3}{8x}-\dfrac{1}{2x}=\dfrac{1}{x^2}\)
c)\(\dfrac{1}{2x}+\dfrac{3}{4x}=\dfrac{5}{2x^2}\)
d) \(\dfrac{2a}{x+a}=1\)
GIẢI CÁC PHƯƠNG TRÌNH SAU:
a, \(\dfrac{315-x}{101}+\dfrac{313-x}{103}+\dfrac{311-x}{105}+\dfrac{309-x}{107}+4=0\)
b, \(\dfrac{x-a}{a-4}+\dfrac{x+a-1}{a+4}+\dfrac{x-a}{16-a^2}=0\)
c, \(\dfrac{x-b-c}{a}+\dfrac{x-c-a}{b}+\dfrac{x-a-b}{c}=3\)
d, \(\dfrac{x-1}{a-1}+\dfrac{1-x}{1+a}-\dfrac{2x-1}{1-a^4}=\dfrac{2a^2\left(x-1\right)}{a^4-1}\)
1. \(\dfrac{5\left(x-1\right)+2}{6}-\dfrac{7x-1}{4}=\dfrac{2\left(2x+1\right)}{7}-5\)
2. \(x-\dfrac{3\left(x+30\right)}{15}-24\dfrac{1}{2}=\dfrac{7x}{10}-\dfrac{2\left(10x+2\right)}{5}\)
3. \(14\dfrac{1}{2}-\dfrac{2\left(x+3\right)}{5}=\dfrac{3x}{2}-\dfrac{2\left(x-7\right)}{3}\)
4. \(\dfrac{x+1}{3}+\dfrac{3\left(2x+1\right)}{4}=\dfrac{2x+3\left(x+1\right)}{6}+\dfrac{7+12x}{12}\)
5. \(\dfrac{3\left(2x-1\right)}{4}-\dfrac{3x+1}{10}+1=\dfrac{2\left(3x+2\right)}{5}\)
6. \(x-\dfrac{3}{17}\left(2x-1\right)=\dfrac{7}{34}\left(1-2x\right)+\dfrac{10x-3}{2}\)
7. \(\dfrac{3\left(x-3\right)}{4}+\dfrac{4x-10,5}{10}=\dfrac{3\left(x+1\right)}{5}+6\)
8. \(\dfrac{2\left(3x+1\right)+1}{4}-5=\dfrac{2\left(3x-1\right)}{5}-\dfrac{3x+2}{10}\)
chứng minh các bất đẳng thức
a/ \(\dfrac{a^2+b^2}{2}\ge\left(\dfrac{a+b}{2}\right)^2\)
c/ \(\dfrac{a^2+b^2+c^2}{3}\ge\left(\dfrac{a+b+c}{3}\right)^2\)
b/ \(\dfrac{a^4+b^4}{2}\ge\left(\dfrac{a+b}{2}\right)^4\)
Giải phương trình:
a) \(\dfrac{x+4}{5}\) - x + 4 = \(\dfrac{x}{3}\) - \(\dfrac{x-2}{2}\)
b) \(\dfrac{4-5x}{6}\) = \(\dfrac{2\left(-x+1\right)}{2}\)
c) \(\dfrac{-\left(x-3\right)}{2}\) - 2 = \(\dfrac{5\left(x+2\right)}{4}\)
d) \(\dfrac{7-3x}{2}\) - \(\dfrac{5+x}{5}\) = 1
CMR: \(\dfrac{a^2}{b^2}+\dfrac{b^2}{c^2}+\dfrac{c^2}{a^2}\ge\dfrac{c}{b}+\dfrac{b}{a}+\dfrac{a}{c}\)
