1) giải phương trình:
a. \(\dfrac{1}{x-5}-\dfrac{3}{x^2-6\text{x}+5}=\dfrac{5}{x-1}\)
b. \(\dfrac{x+5}{x-5}-\dfrac{x-5}{x+5}=\dfrac{20}{x^2-25}\)
c.\(\dfrac{x}{\left(2\text{x}-3\right)}+\dfrac{x}{2\text{x}+2}=\dfrac{2\text{x}}{\left(x+1\right)\left(x-3\right)}\)
d.\(\dfrac{x-1}{x+2}-\dfrac{x}{x-2}=\dfrac{5\text{x}-2}{4-x^2}\)
e. \(\dfrac{1-6\text{x}}{x-2}+\dfrac{9\text{x}+4}{x+2}=\dfrac{x\left(3\text{x}-2\right)+1}{x^2-4}\)
\(\left(\dfrac{\text{√}x}{\text{√}x+2}+\dfrac{8\text{√}x+8}{x+2\text{√}x}-\dfrac{\text{√}x+2}{\text{√}x}\right):\left(\dfrac{x+\sqrt{x}+3}{x+2\sqrt{x}}+\dfrac{1}{\sqrt{x}}\right)\)
a) rút gọn P
b)CMR: P≤1
b) (4√x + 4)/(x + 2√x + 5) ≥ 1
⇔ (4√x + 4)/(x + 2√x + 5) - 1 ≤ 0
Do x ≥ 0 ⇒ x + 2√x + 5 > 0
⇒ (4√x + 4)/(x + 2√x + 5) - 1 ≤ 0
⇔ (4√x + 4) - (x + 2√x + 5) ≤ 0
⇔ 4√x + 4 - x - 2√x - 5 ≤ 0
⇔ -x + 2√x - 1 ≤ 0
⇔ -(x - 2√x + 1) ≤ 0
⇔ -(√x - 1)² ≤ 0 (luôn đúng)
Vậy (4√x + 4)/(x + 2√x + 5) ≤ 1 với mọi x ≥ 0
a: \(P=\dfrac{x+8\sqrt{x}+8-x-4\sqrt{x}-4}{\sqrt{x}\left(\sqrt{x}+2\right)}:\dfrac{x+\sqrt{x}+3+\sqrt{x}+2}{\sqrt{x}\left(\sqrt{x}+2\right)}\)
\(=\dfrac{4\left(\sqrt{x}+1\right)}{x+2\sqrt{x}+5}\)
b: 4(căn x+1)>=4
x+2căn x+5>=5
=>P<=4/5<1
a) 6-7x+7=-8x+12
b) \(\dfrac{\text{4x-1}}{8}\)\(\)=\(\dfrac{6-x}{2}\)-\(\dfrac{1}{4}\)
c) 2x(x-3)+7x-21+0
d) \(\dfrac{x}{x-3}\)+\(\dfrac{x-2}{x+3}\)\(\dfrac{2\left(x^2+6\right)}{x^2-9}\)
P=\(\left(\dfrac{\text{3x^2+ 3x − 3}}{\text{x^2 + x − 2 }}+\dfrac{1}{x-1}+\dfrac{1}{x+2}-2\right):\dfrac{1}{x^2-1}\)
a,rút gọn P
b,tính P với x2-x-6=0
c,tìm x để p>0
Bạn xem lại \(a,b\) mình làm rồi nha.
\(c,P>0\Leftrightarrow\left(x+1\right)^2>0\) (luôn đúng \(\forall x\))
Vậy với mọi giá trị x thì \(P>0\).
rút gọn các biểu thức sau
\(B=\dfrac{3\text{x}^2+6\text{x}+12}{x^3-8\dfrac{ }{ }}\)
C=\(\left(\dfrac{x+1}{2\text{x}-2}+\dfrac{3}{x^2-1}-\dfrac{x+3}{2\text{x}+2}\right).\dfrac{4\text{x}^2-4}{5}\)
E=\(\dfrac{x^2-10\text{x}+25}{x^2-5\text{x}}\)
c: \(E=\dfrac{\left(x-5\right)^2}{x\left(x-5\right)}=\dfrac{x-5}{x}\)
Bài 1.(2,5 điểm)Tìm x, biết:
a) \(\left(2\dfrac{1}{3}+3\dfrac{1}{2}\right).x=-4\dfrac{1}{6}+3\dfrac{1}{2}\)
b) \(\left(1\dfrac{1}{3}+3\dfrac{1}{2}\right).x=4\dfrac{1}{6}-3\dfrac{1}{2}\)
c) \(\dfrac{1}{3}-\dfrac{7}{8}.x=\dfrac{1}{4}\)
d) \(\dfrac{3}{2}.x+\dfrac{1}{7}=\dfrac{7}{8}.\dfrac{64}{49}\)
e) \(5\dfrac{1}{2}-\left(\dfrac{1}{4}.x+\dfrac{2}{5}\right)=25\%\)
c: Ta có: \(\dfrac{1}{3}-\dfrac{7}{8}x=\dfrac{1}{4}\)
\(\Leftrightarrow x\cdot\dfrac{7}{8}=\dfrac{1}{12}\)
\(\Leftrightarrow x=\dfrac{1}{12}\cdot\dfrac{8}{7}=\dfrac{2}{21}\)
d: Ta có: \(\dfrac{3}{2}x+\dfrac{1}{7}=\dfrac{7}{8}\cdot\dfrac{64}{49}\)
\(\Leftrightarrow x\cdot\dfrac{3}{2}=1\)
hay \(x=\dfrac{2}{3}\)
Bài 3:
a) \(\dfrac{2x-1}{5}\)-\(\dfrac{x-2}{3}\)
=\(\dfrac{x+7}{15}\)
b) \(\dfrac{x+3}{2}\)-\(\dfrac{x-1}{3}\)
=\(\dfrac{x+5}{6}\)+1
c) \(\dfrac{2\left(x+5\right)}{3}\)+\(\dfrac{x+12}{2}\)
-\(\dfrac{5\left(x-2\right)}{6}\)=\(\dfrac{x}{3}\)+11
d) \(\dfrac{x-4}{5}\)+\(\dfrac{3x-2}{10}\)-x
=\(\dfrac{2x-5}{3}\)-\(\dfrac{7x+2}{6}\)
e) \(\dfrac{\left(2x-3\right)\left(2x+3\right)}{8}\)
=\(\dfrac{\left(x-4^{ }\right)^2}{6}\)+\(\dfrac{\left(x-2\right)^2}{3}\)
d) \(\dfrac{7x^2-14x-5}{15}\)
=\(\dfrac{\left(2x+1\right)^2}{5}\)-\(\dfrac{\left(x-1\right)^2}{3}\)
e) \(\dfrac{\left(7x+1\right)\left(x-2\right)}{10}\)+\(\dfrac{2}{5}\)
=\(\dfrac{\left(x-2\right)^2}{5}\)+\(\dfrac{\left(x-1\right)\left(x-3\right)}{2}\)
a) Ta có: \(\dfrac{2x-1}{5}-\dfrac{x-2}{3}=\dfrac{x+7}{15}\)
\(\Leftrightarrow\dfrac{3\left(2x-1\right)}{15}-\dfrac{5\left(x-2\right)}{15}=\dfrac{x+7}{15}\)
\(\Leftrightarrow6x-3-5x+10-x-7=0\)
\(\Leftrightarrow0x=0\)(luôn đúng)
Vậy: S={x|\(x\in R\)}
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,\(\dfrac{2x}{3}\)+\(\dfrac{2x-1}{6}\)=4-\(\dfrac{x}{3}\)
6,\(\dfrac{x-1}{2}\)+\(\dfrac{x-1}{4}\)=1-\(\dfrac{2\left(x-1\right)}{3}\)
4, \(\Leftrightarrow4x+4+9\left(2x+1\right)=4x+6\left(x+1\right)+7+12x\)
\(\Leftrightarrow22x+13=22x+13\)vậy pt có vô số nghiệm
5, \(\dfrac{2x}{3}+\dfrac{2x-1}{6}=4-\dfrac{x}{3}\Rightarrow4x+2x-1=24-2x\)
\(\Leftrightarrow8x=25\Leftrightarrow x=\dfrac{25}{8}\)
6, \(\dfrac{x-1}{2}+\dfrac{x-1}{4}=1-\dfrac{2\left(x-1\right)}{3}\Rightarrow6x-6+3x-3=12-8\left(x-1\right)\)
\(\Leftrightarrow9x-9=20-8x\Leftrightarrow17x=29\Leftrightarrow x=\dfrac{29}{17}\)
Bài 1: Tính
a) \(\dfrac{7}{5}+3\dfrac{2}{5}-1\dfrac{1}{2}\)
b) 3 x 2\(\dfrac{4}{9}\)x\(\dfrac{3}{2}\)
c) \(\dfrac{5}{9}x\left(2\dfrac{1}{6}-1\dfrac{2}{3}\right)\)
`a/`
` 7/5 + 3 2/5 - 1 1/2 `
`= (7/5 + 17/5) - 3/2`
`= 24/5 - 3/2 `
`= 48/10 - 15/10 `
`= 33/10 `
`b/`
` 3 xx 2 4/9 xx 3/2 `
` = 3 xx 22/9 xx 3/2 `
` = 22/3 xx 3/2`
`= 11.`
`c/`
` 5/9 xx ( 2 1/6 - 1 2/3 ) `
`= 5/9 xx ( 13/6 -5/3 )`
`= 5/9 xx ( 13/6 - 10/6 ) `
`= 5/9 xx 3/6 `
`= 5/9 xx 1/2 `
`= 5/18`
