Bài 1: 

a) Ta có: \(\dfrac{17}{6}-x\left(x-\dfrac{7}{6}\right)=\dfrac{7}{4}\)

\(\Leftrightarrow\dfrac{17}{6}-x^2+\dfrac{7}{6}x-\dfrac{7}{4}=0\)

\(\Leftrightarrow-x^2+\dfrac{7}{6}x+\dfrac{13}{12}=0\)

\(\Leftrightarrow-12x^2+14x+13=0\)

\(\Delta=14^2-4\cdot\left(-12\right)\cdot13=196+624=820\)

Vì Δ>0 nên phương trình có hai nghiệm phân biệt là:

\(\left\{{}\begin{matrix}x_1=\dfrac{14-2\sqrt{205}}{-24}=\dfrac{-7+\sqrt{205}}{12}\\x_2=\dfrac{14+2\sqrt{2015}}{-24}=\dfrac{-7-\sqrt{205}}{12}\end{matrix}\right.\)

b) Ta có: \(\dfrac{3}{35}-\left(\dfrac{3}{5}-x\right)=\dfrac{2}{7}\)

\(\Leftrightarrow\dfrac{3}{5}-x=\dfrac{3}{35}-\dfrac{10}{35}=\dfrac{-7}{35}=\dfrac{-1}{5}\)

hay \(x=\dfrac{3}{5}-\dfrac{-1}{5}=\dfrac{3}{5}+\dfrac{1}{5}=\dfrac{4}{5}\)

ai giúp mik vs

Bài 3: 

a) Ta có: \(2x-3=x+\dfrac{1}{2}\)

\(\Leftrightarrow2x-x=\dfrac{1}{2}+3\)

\(\Leftrightarrow x=\dfrac{7}{2}\)

b) Ta có: \(4x-\left(x+\dfrac{1}{2}\right)=2x-\left(\dfrac{1}{2}-5\right)\)

\(\Leftrightarrow3x-\dfrac{1}{2}-2x+\dfrac{1}{2}-5=0\)

\(\Leftrightarrow x=5\)

a: Ta có: \(\left(x+2\right)\left(x+3\right)-\left(x-2\right)\left(x-5\right)=-4\)

\(\Leftrightarrow x^2+5x+6-x^2+7x-10=-4\)

\(\Leftrightarrow12x=0\)

hay x=0

b: Ta có: \(\left(x+1\right)\left(x^2-x+1\right)-x\left(x-3\right)\left(x+3\right)=8\)

\(\Leftrightarrow x^3+1-x^3+9x=8\)

\(\Leftrightarrow9x=7\)

hay \(x=\dfrac{7}{9}\)

c: Ta có: \(4x^2-9=\left(3x+1\right)\left(2x-3\right)\)

\(\Leftrightarrow\left(3x+1\right)\left(2x-3\right)-\left(2x-3\right)\left(2x+3\right)=0\)

\(\Leftrightarrow\left(2x-3\right)\left(3x+1-2x-3\right)=0\)

\(\Leftrightarrow\left(2x-3\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=2\end{matrix}\right.\)

`a, 1/2 +x=3/4`

`=> x= 3/4 -1/2`

`=> x= 3/4-2/4`

`=>x= 1/4`

`b, 5/2 -x=1/3`

`=> x= 5/2 -1/3`

`=> x= 15/6 - 2/6`

`=>x= 13/6`

`c, 2 . (1/3 +x)=1/5`

`=> 1/3 +x=1/5:2`

`=> 1/3 +x= 1/10`

`=>x= 1/10-1/3`

`=>x= 3/30 - 10/30`

`=>x=-7/30`

`d, 2/3 - (1/2 -x)=1/5`

`=> 1/2-x= 2/3 -1/5`

`=>1/2-x= 10/15 - 3/15`

`=>1/2-x=7/15`

`=>x= 1/2-7/15`

`=>x=1/30`

`1/2 + x = 3/4`

`=>    x  = 3/4 - 1/2`

`=>    x   = 1/4`

`5/2 - x  = 1/3`

`=>    x  =  5/2 - 1/3`

`=>    x  = 13/6`

`2.(1/3 + x) = 1/5`

`=>1/3 + x  = 1/10 `

`=>         x =  1/10 - 1/3`

`=>        x   = -7/30`

`2/3 - (1/2 -x)= 1/5`

`=>     1/2 - x = 7/15`

`=>             x  = 1/2 - 7/15`

`=>             x  = 1/30`

a. \(\dfrac{1}{2}+x=\dfrac{3}{4}\)

⇔ \(x=\dfrac{3}{4}-\dfrac{1}{2}\)

⇔ \(x=\dfrac{1}{4}\)

b. \(\dfrac{5}{2}-x=\dfrac{1}{3}\)

⇔ \(-x=\dfrac{1}{3}-\dfrac{5}{2}\)

⇔ \(-x=-\dfrac{13}{6}\)

⇔ \(x=\dfrac{13}{6}\)

c. \(2\left(\dfrac{1}{3}+x\right)=\dfrac{1}{5}\)

⇔ \(\dfrac{1}{3}+x=\dfrac{1}{5}\div2\)

⇔ \(x=\dfrac{1}{10}-\dfrac{1}{3}\)

⇔ \(-\dfrac{7}{30}\)

d. \(\dfrac{2}{3}-\left(\dfrac{1}{2}-x\right)=\dfrac{1}{5}\)

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

⇔ \(x=-\dfrac{7}{15}+\dfrac{1}{2}\)

⇔ \(x=\dfrac{1}{30}\)

a: Ta có: \(P=\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{5\sqrt{x}+2}{4-x}\)

\(=\dfrac{x+3\sqrt{x}+2+2x-4\sqrt{x}-5\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

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

\(=\dfrac{3\sqrt{x}}{\sqrt{x}+2}\)

b: Để P=2 thì \(3\sqrt{x}=2\sqrt{x}+4\)

hay x=16

a.1/8+3/8=1/2

b.2/5-1/8=11/40

a, `1/2`

b, `11/40`

1/2

11/40

A nhé

Chọn A

\(a,A=\dfrac{x+\sqrt{x}+2+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}}{\sqrt{x}-2}\\ b,x=36\Leftrightarrow A=\dfrac{6}{6-2}=\dfrac{6}{4}=\dfrac{3}{2}\\ c,A=-\dfrac{1}{3}\Leftrightarrow\dfrac{\sqrt{x}}{\sqrt{x}-2}=-\dfrac{1}{3}\Leftrightarrow3\sqrt{x}=2-\sqrt{x}\\ \Leftrightarrow\sqrt{x}=\dfrac{1}{2}\Leftrightarrow x=\dfrac{1}{4}\left(tm\right)\\ d,A\in Z\Leftrightarrow1+\dfrac{2}{\sqrt{x}-2}\in Z\\ \Leftrightarrow\sqrt{x}-2\inƯ\left(2\right)=\left\{-2;-1;1;2\right\}\\ \Leftrightarrow\sqrt{x}\in\left\{0;1;3;4\right\}\\ \Leftrightarrow x\in\left\{0;1;9;16\right\}\)

\(e,A:B=\dfrac{\sqrt{x}}{\sqrt{x}-2}\cdot\dfrac{\sqrt{x}-2}{\sqrt{x}+1}=\dfrac{\sqrt{x}}{\sqrt{x}+1}=-2\\ \Leftrightarrow\sqrt{x}=-2\sqrt{x}-2\\ \Leftrightarrow\sqrt{x}=-\dfrac{2}{3}\left(ktm\right)\\ \Leftrightarrow x\in\varnothing\)

a: Ta có: \(A=\dfrac{x}{x-4}+\dfrac{1}{\sqrt{x}-2}+\dfrac{1}{\sqrt{x}+2}\)

\(=\dfrac{x+\sqrt{x}+2+\sqrt{x}-2}{x-4}\)

\(=\dfrac{\sqrt{x}}{\sqrt{x}-2}\)

a: \(=\dfrac{x^2+3x+2-x^2+2x+8}{\left(x-2\right)\left(x+2\right)}=\dfrac{5x+10}{\left(x-2\right)\left(x+2\right)}=\dfrac{5}{x-2}\)

b: \(=\dfrac{x^2-4x+3-x^2-3x-2+8x}{\left(x-1\right)\left(x+1\right)}=\dfrac{x+1}{\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x-1}\)

c: \(=\dfrac{x+2}{x\left(x-2\right)}+\dfrac{2}{x\left(x+2\right)}+\dfrac{3x+2}{\left(x+2\right)\left(x-2\right)}\)

\(=\dfrac{x^2+2x+2x-4+3x+2}{x\left(x-2\right)\left(x+2\right)}=\dfrac{x^2+7x-2}{x\left(x-2\right)\left(x+2\right)}\)

a,

\(\dfrac{x+1}{x-2}-\dfrac{x}{x+2}+\dfrac{8}{x^2-4}\\ =\dfrac{x^2+3x+2-x^2+2x+8}{\left(x-2\right)\left(x+2\right)}=\dfrac{5x+10}{\left(x-2\right)\left(x+2\right)}=\dfrac{5\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{5}{x-2}\)

b,

\(\dfrac{x-3}{x+1}-\dfrac{x+2}{x-1}+\dfrac{8x}{x^2-1}\\ =\dfrac{x^2-4x+3-x^2-3x-2+8x}{\left(x-1\right)\left(x+1\right)}=\dfrac{x+1}{\left(x-1\right)\left(x+1\right)}\\ =\dfrac{1}{x-1}\)