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(x-5) . (2x-4)= 0

\(\left[{}\begin{matrix}x-5=0\\2x-4=0\end{matrix}\right.< =>\left[{}\begin{matrix}x=5\\2x=4\end{matrix}\right.< =>\left[{}\begin{matrix}x=5\\x=2\end{matrix}\right.\)

x + 3/4 x 7/10 = 53/40

x + 21/40 = 53/40

x = 53/40 - 21/40

x = 32/40

x = 4/5

34/35 : x = 17/5

x = 34/35 : 17/5

x = 34/35 x 5/17

x = 2/7

x + 3/4 x 7/10 = 53/40

x + ( 3/4 x 7/10 ) = 53/40

x + 21/40 = 53/40 ( tới đây bn cứ lm như bth )

x              = 53/40 - 21/40

x              = 4/5

34/35 : x = 17/5

x             = 34/35 : 17/5

x             = 2/7

\(a,\) \(x+\dfrac{3}{4}\times\dfrac{7}{10}=\dfrac{53}{40}\) 

    \(x+\dfrac{21}{40}=\dfrac{53}{40}\) 

            \(x=\dfrac{53}{40}-\dfrac{21}{40}\) 

            \(x=\dfrac{4}{5}\) 

\(b,\) \(\dfrac{34}{35}:x=\dfrac{17}{5}\) 

            \(x=\dfrac{34}{35}:\dfrac{17}{5}\) 

            \(x=\dfrac{2}{7}\)

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

b: \(=\dfrac{1}{x\left(y-x\right)}-\dfrac{1}{y\left(y-x\right)}\)

\(=\dfrac{y-x}{xy\left(y-x\right)}=\dfrac{1}{xy}\)

c: \(=\dfrac{\left(1-2x\right)\left(1+2x\right)}{x\left(x+4\right)}\cdot\dfrac{3x}{2\left(1-2x\right)}\)

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

d: \(=\dfrac{12x}{8x^3}\cdot\dfrac{15y^4}{5y^3}=\dfrac{3}{2x^2}\cdot3y=\dfrac{9y}{2x^2}\)

f: \(=\dfrac{\left(x-2\right)\left(x+2\right)}{3\left(x+4\right)}\cdot\dfrac{x+4}{2\left(x-2\right)}=\dfrac{x+2}{6}\)

a) \(\left(x-3\right)\left(x+3\right)-\left(x+1\right)^2\) = \(x^2-9-\left(x^2+2x+1\right)\)

\(x^2-9-x^2-2x-1\) = \(-2x-10\)

b) \(\left(4x-3\right)\left(4x+3\right)-16x^2\) = \(16x^2-9-16x^2=-9\)

c) \(\left(x+4\right)\left(x^2-4x+16\right)-x^3\) = \(x^3-4x^2+16x+4x^2-16x+64-x^3\)

= \(64\)

\(a,\left(x-3\right)\left(x+3\right)-\left(x+1\right)^2=x^2-9-x^2-2x-1=-10-2x\) \(b,\left(4x-3\right)\left(4x+3\right)-16x^2=16x^2-9-16x^2=-9\)\(c,\left(x+4\right)\left(x^2-4x+16\right)-x^3=x^3+64-x^3=64\)

f: Ta có: \(16x^2-9\left(x+1\right)^2=0\)

\(\Leftrightarrow\left(4x-3x-3\right)\left(4x+3x+3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(7x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{3}{7}\end{matrix}\right.\)

a,<=> 3x+1/4-2x-3/5=1

<=> x-7/20=1

<=> x= 27/20

a, \(\left(3x+\frac{1}{4}\right)-\frac{1}{3}\left(6x+\frac{9}{5}\right)=1\)

\(3x+\frac{1}{4}-\frac{6}{3}x-\frac{3}{5}=1\)

\(x-\frac{7}{20}=1\Leftrightarrow x=\frac{27}{20}\)

b,ĐKXĐ : x \(\ne\)-1/2 ; 1/2 

 \(\left(\frac{5}{2x+1}\right)-\left(\frac{2x}{1-2x}\right)=1-\left(\frac{6-4x}{4x^2-1}\right)\)

\(\frac{5}{2x+1}-\frac{2x}{1-2x}=1-\frac{6-4x}{4x^2-1}\)

\(\frac{5}{2x+1}-\frac{2x}{1-2x}=1-\frac{2\left(3-2x\right)}{\left(2x+1\right)\left(2x-1\right)}\)

\(\frac{5\left(1-2x\right)\left(2x-1\right)\left(2x+1\right)}{\left(2x+1\right)^2\left(1-2x\right)\left(2x-1\right)}-\frac{2x\left(2x+1\right)^2\left(2x-1\right)}{\left(1-2x\right)\left(2x+1\right)^2\left(2x-1\right)}=\frac{\left(2x+1\right)^2\left(1-2x\right)\left(2x-1\right)}{\left(2x+1\right)^2\left(1-2x\right)\left(2x-1\right)}-\frac{2\left(3-2x\right)\left(2x+1\right)\left(1-2x\right)}{\left(2x+1\right)\left(2x-1\right)^2\left(2x-1\right)\left(1-2x\right)}\)

\(22x-5-20x^2-8x^3=18x-7-8x^3-4x^2\)

lm nốt nha,bị troll rồi ko vt đc nữa.

16x² - (4x+1)² = 0

16x² - (16x²+8x+1) = 0

16x² -16x² - 8x-1=0

-8x-1=0

-8x=1

x= 1/-8

\(\Leftrightarrow-8x-4=0\)

hay \(x=-\dfrac{1}{2}\)

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\(\left(4x+1\right)\left(12x-1\right)\left(3x-2\right)\left(x+1\right)-4\) (Sửa đề)

\(=[\left(4x+1\right)\left(3x+2\right)][\left(12x-1\right)\left(x+1\right)]-4\)

\(=\left(12x^2+11x+2\right)\left(12x^2+11x-1\right)-4\)

Đặt \(12x^2+11x-1=n\)

\(=\left(n+3\right)n-4\)

\(=n^2+3n-4\)

\(=n^2-n+4n-4\)

\(=n\left(n-1\right)+4\left(n-1\right)\)

\(=\left(n-1\right)\left(n+4\right)\)

\(=\left(12x^2+11x-1-1\right)\left(12x^2+11x-1+4\right)\)

\(=\left(12x^2+11x-2\right)\left(12x^2+11x+3\right)\)

\(\left(3x+4\right)\left(x+1\right)\left(6x+7\right)^2=6\)

\(\Leftrightarrow\left(3x^2+7x+4\right)\left(36x^2+84x+49\right)=6\)(1)

Đặt \(\left(3x^2+7x+4\right)=n\)lúc đó (1):

\(\left(12n+1\right)n=6\)

\(\Rightarrow\hept{\begin{cases}n=0,75\\n=\frac{2}{3}\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x=\frac{-2}{3}\\x=\frac{-5}{3}\end{cases}}\)

a)\(4x\left(x-5\right)-\left(x-1\right)\left(4x-3\right)=5\)

    \(4x^2-20x-\left(4x^2-7x+3\right)=5\)

    \(4x^2-20x-4x^2+7x-3=5\)

     \(-13x=8\)

      \(x=-\frac{8}{13}\)

b)\(\left(12x-5\right)\left(4x-1\right)+\left(3x-7\right)\left(1-16x\right)=81\)

     \(48x^2-32x+5+3x-48x^2-7+112x=81\)

     \(83x-2=81\)

     \(x=1\)