c ) \(\frac{x}{5x+5}-\frac{x}{10x-10}\)
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Z
1
LD
19 tháng 7 2017
\(\frac{x^3+2x^2}{2x^2+10x}\)+\(\frac{2x^2-10x+10x-50}{2x^2-10x}\)+\(\frac{50-5x}{2x^2+10x}\)=\(\frac{x^3+4x^2-5x}{2x^2-10x}\)=\(\frac{x\left(x^2+4x-5\right)}{2x\left(x-5\right)}\)=\(\frac{x\left(x-1\right)\left(x-5\right)}{2x\left(x-5\right)}\)=\(\frac{x-1}{2}\)
17 tháng 12 2016
bằng
\(\frac{x}{5\left(x+1\right)}\)-\(\frac{x}{10\left(x-1\right)}\)=\(x\left(\frac{1}{5\left(x+1\right)}-\frac{1}{10\left(x-1\right)}\right)\)=\(x\left(\frac{2\left(x-1\right)}{10\left(x+1\right)\left(x-1\right)}-\frac{x+1}{10\left(x-1\right)\left(x+1\right)}\right)\)
=\(x\left(\frac{2\left(x-1\right)-\left(x+1\right)}{10\left(x+1\right)\left(x-1\right)}\right)\)=\(x\left(\frac{2x-2-x+1}{10\left(x-1\right)\left(x+1\right)}\right)\)=\(x\left(\frac{x-1}{10\left(x-1\right)\left(x+1\right)}\right)\)=\(x\left(\frac{1}{10\left(x+1\right)}\right)\)=\(\frac{x}{10x+10}\)
NH
17 tháng 12 2016
\(\Rightarrow\frac{x}{5\left(x+1\right)}-\frac{x}{10\left(x-1\right)}\)
\(\Leftrightarrow\frac{2x\left(x-1\right)}{10\left(x+1\right)\left(x-1\right)}-\frac{x\left(x+1\right)}{10\left(x-1\right)\left(x+1\right)}\)
\(\Leftrightarrow\frac{2x\left(x-1\right)-x\left(x+1\right)}{10\left(x+1\right)\left(x-1\right)}\)
\(\Leftrightarrow\frac{2x^2-2x-x^2-x}{10\left(x+1\right)\left(x-1\right)}\)\(\Leftrightarrow\frac{x^2-3x}{10\left(x+1\right)\left(x-1\right)}\)
\(\Rightarrow\frac{x}{5x+5}-\frac{x}{10x-10}=\frac{x^2-3x}{10\left(x+1\right)\left(x-1\right)}\)
19 tháng 7 2016
\(a,\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\) (x khác -3; khác 0)
\(=\frac{3}{2\left(x+3\right)}-\frac{x-6}{2x.\left(x+3\right)}=\frac{3x}{2x.\left(x+3\right)}-\frac{x-6}{2x.\left(x+3\right)}=\frac{3x-x+6}{2x.\left(x+3\right)}=\frac{2x+6}{x.\left(2x+6\right)}=\frac{1}{x}\)
19 tháng 7 2016
\(b,\left(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right):\frac{4x}{10x-5}\) (x khác 0 , khác 1/2 khác -1/2 )
\(=\left(\frac{\left(2x+1\right)^2}{\left(2x-1\right)\left(2x+1\right)}-\frac{\left(2x-1\right)^2}{\left(2x-1\right)\left(2x+1\right)}\right).\frac{10x-5}{4x}\)
\(=\left(\frac{4x^2+4x+1}{\left(2x-1\right)\left(2x+1\right)}-\frac{4x^2-4x+1}{\left(2x-1\right)\left(2x+1\right)}\right).\frac{10x-5}{4x}\)
\(=\frac{8x}{\left(2x-1\right)\left(2x+1\right)}.\frac{5.\left(2x-1\right)}{4x}=\frac{10}{2x+1}\)
TD
0
\(\frac{x}{5x+5}-\frac{x}{10x-10}\)
\(=\frac{x}{5\left(x+1\right)}-\frac{x}{10\left(x-1\right)}\)
\(=\frac{2x\left(x-1\right)-x\left(x+1\right)}{10\left(x+1\right)\left(x-1\right)}\)
\(=\frac{2x^2-2x-x^2-x}{10\left(x+1\right)\left(x-1\right)}\)
\(=\frac{x^2-3x}{10\left(x+1\right)\left(x-1\right)}\)