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

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

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

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

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

a)\(dk,x\ne7;x\ne0\)

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

\(=\frac{5x-35}{5x\left(x-7\right)}=\frac{5\left(x-7\right)}{5x\left(x-7\right)}=\frac{1}{x}\)

b)

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

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

a: \(\Leftrightarrow7\left(7-3x\right)+12\left(5x+2\right)=84\left(x+13\right)\)

\(\Leftrightarrow49-21x+60x+24=84x+1092\)

\(\Leftrightarrow39x-84x=1092-73\)

=>-45x=1019

hay x=-1019/45

b: \(\Leftrightarrow21\left(x+3\right)-14=4\left(5x+9\right)-7\left(7x-9\right)\)

=>21x+63-14=20x+36-49x+63

=>21x+49=-29x+99

=>50x=50

hay x=1

c: \(\Leftrightarrow7\left(2x+1\right)-3\left(5x+2\right)=21x+63\)

=>14x+7-15x-6-21x-63=0

=>-22x-64=0

hay x=-32/11

d: \(\Leftrightarrow35\left(2x-3\right)-15\left(2x+3\right)=21\left(4x+3\right)-17\cdot105\)

=>70x-105-30x-45=84x+63-1785

=>40x-150-84x+1722=0

=>-44x+1572=0

hay x=393/11

a, msc 12.7=84 

Chuyển vế về =0 rồi làm

b,msc 28

c,làm tương tự

a, \(\Rightarrow49-21x+60x+24=84x+1092\)

\(\Leftrightarrow-45x=1019\Leftrightarrow x=-\dfrac{1019}{45}\)

b, \(\Rightarrow21\left(x+3\right)-14=4\left(5x+9\right)-7\left(7x-9\right)\)

\(\Leftrightarrow21x+63-14=20x+36-49x+63\)

\(\Leftrightarrow50x=50\Leftrightarrow x=1\)

c, \(\Rightarrow14x+7-15x-6=21x+63\Leftrightarrow-22x=62\Leftrightarrow x=-\dfrac{31}{11}\)

d, \(\Rightarrow35\left(2x-3\right)-15\left(2x+3\right)=21\left(4x+3\right)-105.17\)

\(\Leftrightarrow70x-105-30x-45=84x+63-1785\)

\(\Leftrightarrow-44x=-1572\Leftrightarrow x=\dfrac{393}{11}\)

a,  x - 3 : 2 = 5 14 : 5 12

=>  x - 3 : 2 = 5 2

=>  x - 3 : 2 = 25

=> x – 3 = 25

=> x = 53

b,  30 : x - 7 = 15 19 : 15 18

=>  30 : x - 7 = 15

=> x – 7 = 2

=> x = 9

c,  x 70 = x

=>  x 70 - x = 0

=>  x ( x 69 - 1 ) = 0

=> 

d,  2 x + 1 3 = 9 . 81

=>  2 x + 1 3 = 9 3

=> 2x + 1 = 9

=> x = 4

e,  5 x + 5 x + 2 = 650

=>  5 x 1 + 5 2 = 650

=>  5 x . 26 = 650

=>  5 x = 25

=> x = 2

f,  4 x - 1 2 = 25 . 9

=> 4 x - 1 2 = 5 2 . 3 2

=>  4 x - 1 2 = 15 2

=> 4x – 1 = 15

=> x = 4

a ) \(5x+4=2x+13\)

\(\Leftrightarrow5x-2x=13-4\)

\(\Leftrightarrow3x=9\)

\(\Leftrightarrow x=3\)

Vậy tập nghiệm của phương trình là S = {3}

b ) \(\left(x+2\right)\left(x-7\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x-7=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=7\end{matrix}\right.\)

Vậy tập nghiệm của phương trình là \(S=\left\{-2;7\right\}\)

c ) \(\left|x-2\right|=2x+14\) ( 1 )

+ ) \(\left|x-2\right|=x-2\). Khi \(x-5\ge0\Leftrightarrow x\ge5\)

\(\left(1\right)\Leftrightarrow x-2=2x+14\)

\(\Leftrightarrow x-2x=14+2\)

\(\Leftrightarrow-x=16\Leftrightarrow x=-16\) ( Loại )

+ ) \(\left|x-5\right|=-x+5.\) Khi \(x-5< 0\Leftrightarrow x< 5\)

\(\left(1\right)\Leftrightarrow-x+2=2x+14\)

\(\Leftrightarrow-3x=12\)

\(\Leftrightarrow x=-4\) ( Thõa mãn )

Vậy ................

d ) \(4x-7< 17-2x\)

\(\Leftrightarrow4x+2x< 17+7\)

\(\Leftrightarrow6x< 24\)

\(\Leftrightarrow x< 4\)

Vậy ........

a) 5x + 4 = 2x +13

<=> 5x - 2x = 13- 4

<=> 3x = 9

<=> x = 3

Vậy phương trình có tập nghiệm S = { 3 }

b) (x+2). (x-7) = 0

=> \(\left[{}\begin{matrix}x+2=0\\x-7=0\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x=-2\\x=7\end{matrix}\right.\)

Vậy phương trình có tập nghiệm S= { -2;7}

c)

khi x \(\ge\) 2 thì\(\left|x-2\right|\) = x - 2 khi đó phương trình có dạng :

x - 2 = 2x + 14

<=> x - 2x = 14+2

<=> -x = 16

<=> -x. (-1)= 16. (-1)

<=> x = -16 (loại )

khi x < 2 thì \(\left|x-2\right|\) = -x + 2 khi đó phương trình có dạng :

-x + 2 = 2x + 14

<=> -x - 2x = 14-2

<=> -3x = 12

<=> x = -4 (nhận)

Vậy phương trình có tập nghiệm S= { -4 }