\(1,\\ a,\Leftrightarrow x-\dfrac{1}{3}=0\Leftrightarrow x=\dfrac{1}{3}\\ b,\Leftrightarrow\left[{}\begin{matrix}x-4=4\\x-4=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=0\end{matrix}\right.\\ c,\Leftrightarrow2x+1=-2\Leftrightarrow x=-\dfrac{3}{2}\\ 2,\\ a,=1\\ b,=\left(\dfrac{13}{4}\right)^2=\dfrac{169}{16}\\ c,=\left(-\dfrac{7}{4}\right)^2=\dfrac{49}{16}\\ d,=\left(\dfrac{3}{7}\right)^{20}:\left(\dfrac{3}{7}\right)^{12}=\left(\dfrac{3}{7}\right)^8=...\\ e,=\left(3\cdot5\cdot\dfrac{2}{3}\right)^2=10^2=100\)

\(A=\left(x+2\right)^2-\left(x+3\right)\left(x-1\right)+15\)

\(A=x^2+4x+4-\left(x^2-x+3x-3\right)+15\)

\(A=\left(x^2-x^2\right)+\left(4x+x-3x\right)+\left(15+3+4\right)\)

\(A=2x+22\)

______________________

\(B=\left(x+1\right)\left(x-1\right)-\left(x+4\right)^2-6\)

\(B=\left(x^2-1\right)-\left(x^2+8x+16\right)-6\)

\(B=\left(x^2-x^2\right)-8x-\left(1+16+6\right)\)

\(B=-8x-23\)

_________________

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

\(C=\left[\left(3x\right)^2-2^2\right]-\left(9x^2-6x+1\right)\)

\(C=\left(9x^2-9x^2\right)+6x-\left(4+1\right)\)

\(C=6x-5\)

a) Rút gọn biểu thức A = (x + 2)2 - (x + 3)(x - 1) + 15:

Bắt đầu bằng việc mở ngoặc:
A = (x^2 + 4x + 4) - (x^2 + 2x - 3x - 3) + 15

Tiếp theo, kết hợp các thành phần tương tự:
A = x^2 + 4x + 4 - x^2 - 2x + 3x + 3 + 15

Tiếp tục đơn giản hóa:
A = x^2 - x^2 + 4x - 2x + 3x + 4 + 3 + 15

Kết quả cuối cùng:
A = 5x + 19

b) Rút gọn biểu thức B = (x - 1)(x + 1) - (x + 4)2 - 6:

Bắt đầu bằng việc mở ngoặc:
B = (x^2 - 1) - (x^2 + 4x + 4) - 6

Tiếp theo, kết hợp các thành phần tương tự:
B = x^2 - 1 - x^2 - 4x - 4 - 6

Tiếp tục đơn giản hóa:
B = x^2 - x^2 - 4x - 4 - 6 - 1

Kết quả cuối cùng:
B = -4x - 11

c) Rút gọn biểu thức C = (3x - 2)(3x + 2) - (3x - 1)2:

Bắt đầu bằng việc mở ngoặc:
C = (9x^2 - 4) - (9x^2 - 6x + 1)

Tiếp theo, kết hợp các thành phần tương tự:
C = 9x^2 - 4 - 9x^2 + 6x - 1

Tiếp tục đơn giản hóa:
C = 9x^2 - 9x^2 + 6x - 4 - 1

Kết quả cuối cùng:
C = 6x - 5

a: =2/5-3/5+3/7=3/7-1/5

=15/35-7/35

=8/35

b: =>5/7:x=4/3

=>x=5/7:4/3=5/7*3/4=15/28

c: =>x-1/3=15/8:4/5=15/8*5/4=75/32

=>x=75/32+1/3=257/96

d: =>2x+1/8=2/7

=>2x=9/56

=>x=9/112

e: =>2x=10/3-5/4-3/4=10/3-2=4/3

=>x=2/3

\(a,\dfrac{2}{5}+\dfrac{3}{7}+\left(-\dfrac{3}{5}\right)\\ =\dfrac{2}{5}+\dfrac{3}{7}-\dfrac{3}{5}\\=\left(\dfrac{2}{5}-\dfrac{3}{5}\right)+\dfrac{3}{7}\\ =-\dfrac{1}{5}+\dfrac{3}{7}\\ =-\dfrac{7}{35}+\dfrac{15}{35}\\ =\dfrac{8}{35}\\ b,1-\dfrac{5}{7}:x=-\dfrac{1}{3}\\ =>\dfrac{5}{7}:x=1-\left(-\dfrac{1}{3}\right)\\ =>\dfrac{5}{7}:x=1+\dfrac{1}{3}\\ =>\dfrac{5}{7}:x=\dfrac{3}{3}+\dfrac{1}{3}\\ =>\dfrac{5}{7}:x=\dfrac{4}{3}\\ =>x=\dfrac{5}{7}:\dfrac{4}{3}\\ =>x=\dfrac{5}{7}.\dfrac{3}{4}\\ =>x=\dfrac{15}{28}\\ c,\dfrac{4}{5}\left(x-\dfrac{1}{3}\right)=\dfrac{15}{8}\\ =>x-\dfrac{1}{3}=\dfrac{15}{8}:\dfrac{4}{5}\\ =>x-\dfrac{1}{3}=\dfrac{15}{8}.\dfrac{5}{4}\\ =>x-\dfrac{1}{3}=\dfrac{75}{32}\\ =>x=\dfrac{75}{32}+\dfrac{1}{3}\\ =>x=\dfrac{257}{96}\)

\(d,\dfrac{2}{3}:\left(2x+\dfrac{1}{8}\right)=\dfrac{7}{3}\\ =>2x+\dfrac{1}{8}=\dfrac{2}{3}:\dfrac{7}{3}\\ =>2x+\dfrac{1}{8}=\dfrac{2}{3}.\dfrac{3}{7}\\ =>2x+\dfrac{1}{8}=\dfrac{2}{7}\\ =>2x=\dfrac{2}{7}-\dfrac{1}{8}\\ =>2x=\dfrac{16}{56}-\dfrac{7}{56}\\ =>2x=\dfrac{9}{56}\\ =>x=\dfrac{9}{56}:2\\ =>x=\dfrac{9}{112}\\ e,2x+\dfrac{3}{4}=\dfrac{10}{3}-\dfrac{5}{4}\\ =>e,2x+\dfrac{3}{4}=\dfrac{40}{12}-\dfrac{15}{12}\\ =>2x+\dfrac{3}{4}=\dfrac{25}{12}\\ =>2x=\dfrac{25}{12}-\dfrac{3}{4}\\ =>2x=\dfrac{25}{12}-\dfrac{9}{12}\\ =>2x=\dfrac{16}{12}\\ =>2x=\dfrac{4}{3}\\ =>x=\dfrac{4}{3}:2\\ =>x=\dfrac{4}{6}\\ =>x=\dfrac{2}{3}\)