7x-26/x-1 = 2/3
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2: =(2x+1)^2-y^2
=(2x+1+y)(2x+1-y)
3: =x^2(x^2+2x+1)
=x^2(x+1)^2
4: =x^2+6x-x-6
=(x+6)(x-1)
5: =-6x^2+3x+4x-2
=-3x(2x-1)+2(2x-1)
=(2x-1)(-3x+2)
6: =5x(x+y)-(x+y)
=(x+y)(5x-1)
7: =2x^2+5x-2x-5
=(2x+5)(x-1)
8: =(x^2-1)*(x^2-4)
=(x-1)(x+1)(x-2)(x+2)
9: =x^2(x-5)-9(x-5)
=(x-5)(x-3)(x+3)
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\(x^2-11x-26=0\)
\(x^2-13x+2x-26=0\)
\(x.\left(x-13\right)+2.\left(x-13\right)=0\)
\(\left(x+2\right).\left(x-13\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+2=0\\x-13=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-2\\x=13\end{cases}}\)
vậy...
P/S: lớp 7 sai sót mong thông cảm
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\(2\)
CMR
\(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+....+\frac{1}{49.50}=\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+...+\frac{1}{50}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=\left(\frac{1}{1}+\frac{1}{3}+...+\frac{1}{49}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)\)
\(=\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{49}+\frac{1}{50}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)\)
\(=\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{50}-1-\frac{1}{2}-\frac{1}{3}-...-\frac{1}{25}\)
\(=\frac{1}{26}+\frac{1}{27}+....+\frac{1}{50}\left(đpcm\right)\)
=>21x-78=2x-2
=>19x=76
=>x=4
\(\dfrac{7x-26}{x-1}=\dfrac{2}{3}đkxđ\left(x\ne1\right)\\ \Leftrightarrow\dfrac{3\left(7x-26\right)}{3\left(x-1\right)}=\dfrac{2\left(x-1\right)}{3\left(x-1\right)}\\ \Rightarrow3\left(7x-26\right)=2\left(x-1\right)\\ \Leftrightarrow21x-78=2x-2\\ \Leftrightarrow21x-2x=-2+78\\ \Leftrightarrow19x=76\\ \Leftrightarrow x=4\)
Vậy pt có nghiệm `x=4`