\(b,\dfrac{1}{5}:x=\dfrac{1}{5}-\dfrac{1}{7}\)

\(\dfrac{1}{5}:x=\dfrac{7}{35}-\dfrac{5}{35}\)

\(\dfrac{1}{5}:x=\dfrac{2}{35}\)

\(x=\dfrac{1}{5}:\dfrac{2}{35}\)

\(x=\dfrac{1}{5}.\dfrac{35}{2}\)

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

\(x-\left(\dfrac{50x}{100}+\dfrac{25x}{100}\right)=11\dfrac{1}{4}\)

\(x-\dfrac{3x}{4}=\dfrac{45}{4}\)

\(\dfrac{x}{4}=\dfrac{45}{4}\Rightarrow x=45\)

Ta có: \(x-\left(\dfrac{50x}{100}+\dfrac{25x}{200}\right)=11\dfrac{1}{4}\)

\(\Leftrightarrow x-\dfrac{1}{2}x-\dfrac{1}{8}x=\dfrac{45}{4}\)

\(\Leftrightarrow x\cdot\dfrac{3}{8}=\dfrac{45}{4}\)

hay x=30

<=>\(x+x-\frac{25x}{100}-\frac{25}{100}=60\)

<=>\(2x-\frac{50x}{100}=60\)

<=>\(\frac{150x}{100}=60\)

<=> 150x=6000

<=> x=40

1) ĐKXĐ: \(x\ge-2\)

\(pt\Leftrightarrow\dfrac{\sqrt{x+2}}{2}+5\sqrt{x+2}-2\sqrt{x+2}=14\)

\(\Leftrightarrow\dfrac{\sqrt{x+2}+6\sqrt{x+2}}{2}=14\Leftrightarrow7\sqrt{x+2}=28\)

\(\Leftrightarrow\sqrt{x+2}=4\Leftrightarrow x+2=16\Leftrightarrow x=14\left(tm\right)\)

2) ĐKXĐ: \(x\ge0\)

\(pt\Leftrightarrow2x+3=x^2\Leftrightarrow\left(x-3\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=-1\left(ktm\right)\end{matrix}\right.\)

3) \(pt\Leftrightarrow\sqrt{\left(5x+2\right)^2}=1\Leftrightarrow\left|5x+2\right|=1\)

\(\Leftrightarrow\left[{}\begin{matrix}5x+2=1\\5x+2=-1\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{5}\\x=-\dfrac{3}{5}\end{matrix}\right.\)

4) ĐKXĐ: \(\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1\ge0\\2x-1>0\end{matrix}\right.\\\left\{{}\begin{matrix}x+1\le0\\2x-1< 0\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{1}{2}\\x\le-1\end{matrix}\right.\)

\(pt\Leftrightarrow\dfrac{x+1}{2x-1}=4\Leftrightarrow x+1=8x-4\)

\(\Leftrightarrow7x=5\Leftrightarrow x=\dfrac{5}{7}\left(tm\right)\)

5) ĐKXĐ: \(x\ge2\)

\(pt\Leftrightarrow\dfrac{x-2}{3x+1}=36\)

\(\Leftrightarrow x-2=108x+36\Leftrightarrow107x=-38\Leftrightarrow x=-\dfrac{38}{107}\left(ktm\right)\)

Vậy \(S=\varnothing\)

`a)1/[x-5x^2]-[25x-15]/[25x^2-1]`

`=[-(5x+1)-x(25x-15)]/[x(5x-1)(5x+1)]`

`=[-5x-1-25x^2+15x]/[x(5x-1)(5x+1)]`

`=[-25x^2+10x-1]/[x(5x-1)(5x+1)]`

`=[-(5x-1)^2]/[x(5x-1)(5x+1)]`

`=[1-5x]/[x(5x+1)]`

________________________________________________-

`b)(-1/[x^2-4x]+2/[16-x^2]-[-1]/[4x+16]):1/[4x]`

`=[-4(x+4)-8x+x(x-4)]/[4x(x-4)(x+4)].4x`

`=[-4x-16-8x+x^2-4x]/[(x-4)(x+4)]`

`=[x^2-16x-16]/[x^2-16]`

a) Ta có: \(2\sqrt{9x-27}-\dfrac{1}{5}\sqrt{25x-75}-\dfrac{1}{7}\sqrt{49x-147}=20\)

\(\Leftrightarrow6\sqrt{x-3}-\sqrt{x-3}-\sqrt{x-3}=20\)

\(\Leftrightarrow4\sqrt{x-3}=20\)

\(\Leftrightarrow x-3=25\)

hay x=28

b) Ta có: \(\sqrt{9x+18}-5\sqrt{x+2}+\dfrac{4}{5}\sqrt{25x+50}=6\)

\(\Leftrightarrow3\sqrt{x+2}-5\sqrt{x+2}+4\sqrt{x+2}=6\)

\(\Leftrightarrow2\sqrt{x+2}=6\)

\(\Leftrightarrow x+2=9\)

hay x=7

a, \(\dfrac{4x+13}{5x\left(x-7\right)}-\dfrac{x-48}{5x\left(7-x\right)}\)

\(=\dfrac{4x+13}{5x\left(x-7\right)}+\dfrac{x-48}{5x\left(x-7\right)}\)

\(=\dfrac{4x+13+x-48}{5x\left(x-7\right)}\)

\(=\dfrac{5x-35}{5x\left(x-7\right)}\)

\(=\dfrac{5\left(x-7\right)}{5x\left(x-7\right)}=\dfrac{1}{x}\)

b, \(\dfrac{1}{x-5x^2}-\dfrac{25x-15}{25x^2-1}\)

\(=\dfrac{1}{x\left(1-5x\right)}+\dfrac{25x-15}{\left(1-5x\right)\left(1+5x\right)}\)

\(=\dfrac{1+5x}{x\left(x-5x\right)\left(1+5x\right)}+\dfrac{x\left(25x-15\right)}{x\left(1-5x\right)\left(1+5x\right)}\)

\(=\dfrac{1+5x+25x^2-15x}{x\left(1-5x\right)\left(1+5x\right)}\)\(=\dfrac{25x^2-10x+1}{x\left(1-5x\right)\left(1+5x\right)}=\dfrac{\left(5x-1\right)^2}{x.\left(1-5x\right)\left(1+5x\right)}\)

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

x=24

=> x+1=25

=> M=x¹⁰⁰-(x+1)x⁹⁹+(x+1)x⁹⁸-(x+1)x⁹⁷+(x+1)x⁹⁶-...-(x+1)x³+(x+1)x²-(x+1)x+25

       =x¹⁰⁰-x¹⁰⁰-x⁹⁹+x⁹⁹+x⁹⁸-x⁹⁸-x⁹⁷+x⁹⁷+x⁹⁶-...-x⁴-x³+x³+x²-x²-x+25

       =-x+25

       =-24+25

       =1

Vậy M=1.

\(a=\dfrac{2010}{x^2-2x+1001}=\dfrac{2010}{x^2-2x+1+1000}=\dfrac{2010}{\left(x-1\right)^2+1000}\le\dfrac{101}{100}\)

\(b=\dfrac{1000}{x^2+y^2-20\left(x+y\right)+2210}=\dfrac{1000}{x^2+y^2-20x-20y+2210}=\dfrac{1000}{x^2+y^2-20x-20y+100+100+2010}=\dfrac{1000}{\left(x-10\right)^2+\left(y-10\right)^2+2010}\le\dfrac{100}{201}\)

\(c=\dfrac{100}{25x^2-20x+14}=\dfrac{100}{25x^2-20x+4+10}=\dfrac{10}{\left(5x-2\right)^2+10}\le1\)