\(A=\dfrac{6x}{5x-20}-\dfrac{x}{x^2-8x+16}\)

\(ĐKXĐ:x\ne\pm4\)

\(\Leftrightarrow A=\dfrac{6x}{5\left(x-4\right)}-\dfrac{x}{\left(x-4\right)^2}\)

\(\Leftrightarrow A=\dfrac{6x^2-24x-5x}{5\left(x-4\right)^2}\)

\(\Leftrightarrow\dfrac{6x^2-29x}{5\left(x-4\right)^2}\)

\(\Leftrightarrow\dfrac{x\left(6x-29\right)}{5\left(x-4\right)^2}\)

\(A=\left(\dfrac{x}{x-1}-\dfrac{x+1}{x}\right):\left(\dfrac{x}{x+1}-\dfrac{x-1}{x}\right)\)

\(ĐKXĐ:x\ne0;x\ne\pm1\)

\(\Leftrightarrow A=\left(\dfrac{x^2}{x\left(x-1\right)}-\dfrac{x^2-1}{x\left(x-1\right)}\right):\left(\dfrac{x^2}{x\left(x+1\right)}-\dfrac{x^2-1}{x\left(x+1\right)}\right)\)

\(\Leftrightarrow A=\dfrac{x\left(x+1\right)}{x\left(x-1\right)}\)

\(\Leftrightarrow A=\dfrac{x+1}{x-1}\)

\(A=\left[\dfrac{6x+1}{x^2-6x}+\dfrac{6x-1}{x^2+6x}\right].\dfrac{x^2-36}{x^2+1}\)

\(ĐKXĐ:x\ne0;x\ne\pm6\)

\(\Leftrightarrow A=\left[\dfrac{6x+1}{x\left(x-6\right)}+\dfrac{6x-1}{x\left(x+6\right)}\right].\dfrac{\left(x-6\right)\left(x+6\right)}{x^2+1}\)

\(\Leftrightarrow A=\left[\dfrac{\left(6x+1\right)\left(x+6\right)+\left(6x-1\right)\left(x-6\right)}{x\left(x-6\right)\left(x+6\right)}\right].\dfrac{\left(x-6\right)\left(x+6\right)}{x^2+1}\)

\(\Leftrightarrow A=\left[\dfrac{6x^2+37x+6+6x^2-37x+6}{x\left(x-6\right)\left(x+6\right)}\right].\dfrac{\left(x-6\right)\left(x+6\right)}{x^2+1}\)

\(\Leftrightarrow A=\dfrac{12\left(x^2+1\right)}{x\left(x-6\right)\left(x+6\right)}.\dfrac{\left(x-6\right)\left(x+6\right)}{x^2+1}\)

\(\Leftrightarrow A=\dfrac{12}{x}\)

đề là mô thế bợn ơi!!!!!!!!!!

a: \(=\dfrac{6x}{5\left(x-4\right)}-\dfrac{x}{\left(x-4\right)^2}\)

\(=\dfrac{6x^2-24x-5x}{5\left(x-4\right)^2}=\dfrac{6x^2-29x}{5\left(x-4\right)^2}\)

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

\(=\dfrac{4x-8+3x+6-5x-2}{\left(x+2\right)\left(x-2\right)}-\dfrac{1}{x+2}\)

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

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

c: \(\left(\dfrac{x}{x-1}-\dfrac{x+1}{x}\right):\left(\dfrac{x}{x+1}-\dfrac{x-1}{x}\right)\)

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

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

bài 5:

1: \(\dfrac{12x^3y^2}{18xy^5}=\dfrac{12x^3y^2:6xy^2}{18xy^5:6xy^2}=\dfrac{2x^2}{3y^3}\)

2: \(\dfrac{10xy-5x^2}{2x^2-8y^2}=\dfrac{5x\cdot2y-5x\cdot x}{2\left(x^2-4y^2\right)}\)

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

3: \(\dfrac{x^2-xy-x+y}{x^2+xy-x-y}\)

\(=\dfrac{\left(x^2-xy\right)-\left(x-y\right)}{\left(x^2+xy\right)-\left(x+y\right)}\)

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

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

\(=\dfrac{\left(x+1\right)\left(x-1\right)^2}{6\left(x^2-1\right)\left(x-1\right)\left(x^2+x+1\right)}\)

\(=\dfrac{\left(x+1\right)\left(x-1\right)}{6\left(x-1\right)\left(x+1\right)\cdot\left(x^2+x+1\right)}\)

\(=\dfrac{1}{6\left(x^2+x+1\right)}\)

5: \(\dfrac{2x^2-7x+3}{1-4x^2}\)

\(=-\dfrac{2x^2-7x+3}{4x^2-1}\)

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

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

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

Bài 3:

1: \(9x^3-xy^2\)

\(=x\cdot9x^2-x\cdot y^2\)

\(=x\left(9x^2-y^2\right)\)

\(=x\left(3x-y\right)\left(3x+y\right)\)

2: \(x^2-3xy-6x+18y\)

\(=\left(x^2-3xy\right)-\left(6x-18y\right)\)

\(=x\left(x-3y\right)-6\left(x-3y\right)\)

\(=\left(x-3y\right)\left(x-6\right)\)

3: \(x^2-3xy-6x+18y\)

\(=\left(x^2-3xy\right)-\left(6x-18y\right)\)

\(=x\left(x-3y\right)-6\left(x-3y\right)\)

\(=\left(x-3y\right)\left(x-6\right)\)

4: \(6xy-x^2+36-9y^2\)

\(=36-\left(x^2-6xy+9y^2\right)\)

\(=36-\left(x-3y\right)^2\)

\(=\left(6-x+3y\right)\left(6+x-3y\right)\)

5: \(x^4-6x^2+5\)

\(=x^4-x^2-5x^2+5\)

\(=x^2\left(x^2-1\right)-5\left(x^2-1\right)\)

\(=\left(x^2-5\right)\left(x^2-1\right)\)

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

6: \(9x^2-6x-y^2+2y\)

\(=\left(9x^2-y^2\right)-\left(6x-2y\right)\)

\(=\left(3x-y\right)\left(3x+y\right)-2\left(3x-y\right)\)

\(=\left(3x-y\right)\left(3x+y-2\right)\)

a: Ta có: \(x^2-4-\left(x+2\right)^2\)

\(=x^2-4-x^2-4x-4\)

=-4x-8

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

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

=2x-1

c: ta có: \(\left(x-2\right)\left(x+2\right)-\left(x-2\right)\left(x+5\right)\)

\(=\left(x-2\right)\left(x+2-x-5\right)\)

\(=-3x+6\)

d: Ta có: \(\left(6x+1\right)^2-2\left(6x+1\right)\left(6x-1\right)+\left(6x-1\right)^2\)

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

=4

e: ta có: \(7a\left(3a-5\right)+\left(2a-3\right)\left(4a+1\right)-\left(6a-2\right)^2\)

\(=21a^2-35a+8a^2+2a-12a-3-\left(36a^2-24a+4\right)\)

\(=29a^2-45a-3-36a^2+24a-4\)

\(=-7a^2-21a-7\)

g: ta có: \(\left(5y-3\right)\left(5y+3\right)-\left(5y-4\right)^2\)

\(=25y^2-9-25y^2+40y-16\)

=40y-25

h: Ta có: \(\left(3x+1\right)^3-\left(1-2x\right)^3\)

\(=27x^3+27x^2+9x+1-1+6x-12x^2+8x^3\)

\(=35x^3+15x^2+15x\)

i: Ta có: \(\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)

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

\(=16x^2\)

1/ \(x^4+x^2-2=0\)

\(\Leftrightarrow\left(x^2\right)^2-x^2+2x^2-2=0\\ \Leftrightarrow x^2\left(x^2-1\right)+2\left(x^2-1\right)=0\\ \Leftrightarrow\left(x^2+2\right)\left(x^2-1\right)=0\\ \Leftrightarrow\left(x^2+2\right)\left(x-1\right)\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2+2=0\\x+1=0\\x-1-0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)

2/ \(x^3+3x^2+6x+4=0\)

\(\Leftrightarrow\left(x^3+x^2\right)+\left(2x^2+2x\right)+\left(4x+4\right)=0\\ \Leftrightarrow x^2\left(x+1\right)+2x\left(x+1\right)+4\left(x+1\right)=0\\ \Leftrightarrow\left(x+1\right)\left(x^2+2x+4\right)=0\)

\(\Leftrightarrow x+1=0\) (do \(x^2+2x+4=\left(x+1\right)^2+3>0,\forall x\))

\(\Leftrightarrow x=-1\).

3/ \(x^3-6x^2+8x=0\)

\(\Leftrightarrow x\left(x^2-6x+8\right)=0\\ \Leftrightarrow x\left[\left(x^2-2x\right)-\left(4x-8\right)\right]=0\\ \Leftrightarrow x\left[x\left(x-2\right)-4\left(x-2\right)\right]=0\\ \Leftrightarrow x\left(x-2\right)\left(x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x-2=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\\x=4\end{matrix}\right.\)

4/ \(x^4-8x^3-9x^2=0\)

\(\Leftrightarrow x^2\left(x^2-8x-9\right)=0\\ \Leftrightarrow x^2\left(x^2-9x+x-9\right)=0\\ \Leftrightarrow x^2\left(x\left(x-9\right)+\left(x-9\right)\right)=0\\ \Leftrightarrow x^2\left(x+1\right)\left(x-9\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2=0\\x+1=0\\x-9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\\x=9\end{matrix}\right.\)

a) Ta có: \(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)

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

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

b) Ta có: \(x\left(2x^2-3\right)-x^2\left(5x+1\right)+x^2\)

\(=2x^3-3x-5x^3-x^2+x^2\)

\(=-3x-3x^3\)

c) Ta có: \(3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)

\(=3x^2-6x-5x+5x^2-8x^2+24\)

\(=24-11x\)

d) Ta có: \(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)

\(=2^{32}-1\)

a,\(A=\left(x^4-3x^2+9\right)\left(x^2+3\right)+\left(3-x^2\right)^2\)

\(A=x^6-3x^4+9x^2+3x^4-9x^2+27+9-6x^2+x^4\)

\(A=x^6+x^4-6x^2+36\)

b, \(M=5\left(x+2y\right)^2-\left(3y+2x\right)^2+\left(4x-y\right)^2+3\left(x-2y\right)\left(x+2y\right)\)

\(M=5\left(x^2+4xy+4y^2\right)-\left(9y^2+12xy+4x^2\right)+\left(16x^2-8xy+y^2\right)+3\left(x^2-4y^2\right)\)

\(M=5x^2+20xy+20y^2-9y^2-12xy-4x^2+16x^2-8xy+y^2+3x^2-12y^2\)

\(M=20x^2\)

Các câu còn lại làm tương tự! Chúc bạn học tốt!!!

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

\(\Leftrightarrow\left(6x+1\right)^2-2\left(1+6x\right)\left(6x-1\right)+\left(6x-1\right)^2\)

\(\Leftrightarrow\left[\left(6x+1\right)-\left(6x-1\right)\right]^2\)

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