Thực hiện phép tính a)\(\frac{x+2}{x-3}+\frac{x^2+6}{x^2-3x}\)
b)\(\frac{4x-4}{x^2-4x+4}:\frac{x^2-1}{\left(2-x\right)^2}\)
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Những câu hỏi liên quan
9 tháng 12 2019
\(\frac{3\left(x+1\right)}{x+2}-\frac{3x-6}{x^2-4}\)
\(=\frac{3\left(x+1\right)}{x+2}-\left(\frac{3x-6}{x^2-4}\right)\)
\(=\frac{3x^2-6x^2-12x+24}{x^3+2x^2-4x-8}\)
\(=\frac{3\left(x+2\right)\left(x-2\right)\left(x-2\right)}{\left(x+2\right)\left(x+2\right)\left(x-2\right)}\)
\(=\frac{3x-6}{x+2}\)
9 tháng 12 2019
\(\frac{x^2+4x+4}{1-x}.\frac{\left(1-x\right)^2}{3\left(x+2\right)^3}\)
\(=\frac{x^2+4x+4}{1-x}.\left[\frac{\left(1-x\right)^2}{3\left(x+2\right)^3}\right]\)
\(=\frac{x^4+2x^3-3x^2-4x+4}{-3x^4-15x^3-18x^2+12x+24}\)
\(=\frac{\left(x-1\right)\left(x-1\right)\left(x+2\right)\left(x+2\right)}{3\left(-x+1\right)\left(x+2\right)\left(x+2\right)\left(x+2\right)}\)
\(=\frac{-x+1}{3x+6}\)
26 tháng 7 2017
Ta có \(\left(\frac{1}{x^2+4x+4}-\frac{1}{x^2-4x+4}\right):\left(\frac{1}{x+2}+\frac{1}{x-2}\right)\)
\(=\frac{\left(x-2\right)^2-\left(x+2\right)^2}{\left(x-2\right)^2\left(x+2\right)^2}:\frac{x-2+x+2}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{\left(x-2+x+2\right)\left(x-2-x-2\right)}{\left(x-2\right)^2\left(x+2\right)^2}:\frac{2x}{\left(x+2\right)\left(x-2\right)}\)
\(\frac{-4.2x}{\left(x+2\right)^2\left(x-2\right)^2}.\frac{\left(x+2\right)\left(x-2\right)}{2x}=\frac{-4}{\left(x+2\right)\left(x-2\right)}\)
15 tháng 7 2017
a) ĐKXĐ: \(x;y\ne0,x\ne\frac{y}{2},y\ne\frac{x}{2}\)
\(\frac{y}{2x^2-xy}+\frac{4x}{y^2-2xy}=\frac{y}{x\left(2x-y\right)}-\frac{4x}{y\left(2x-y\right)}\)\(=\frac{y^2-4x^2}{xy\left(2x-y\right)}=\frac{\left(y-2x\right)\left(y+2x\right)}{xy\left(2x-y\right)}\)
\(=\frac{-\left(y+2x\right)}{xy}\)
b) ĐKXĐ: \(x\ne2;x\ne-2\)
\(\frac{1}{x+2}+\frac{3}{x^2-4}+\frac{x-14}{\left(x^2+4x+4\right)\left(x-2\right)}\)\(=\frac{1}{x+2}+\frac{3}{\left(x-2\right)\left(x+2\right)}+\frac{x-14}{\left(x+2\right)^2\left(x-2\right)}\)
\(=\frac{\left(x-2\right)\left(x+2\right)+3\left(x+2\right)+x-14}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{x^2-4+3x+6+x-14}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{x^2+4x-12}{\left(x+2\right)^2\left(x-2\right)}=\frac{\left(x^2+4x+4\right)-16}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{\left(x+2\right)^2-16}{\left(x+2\right)^2\left(x-2\right)}=\frac{\left(x+2-4\right)\left(x+2+4\right)}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{\left(x-2\right)\left(x+6\right)}{\left(x+2\right)^2\left(x-2\right)}=\frac{x+6}{\left(x+2\right)^2}\)
CC
20 tháng 2 2020
\(ĐKXĐ:x\ne\pm2\)
\(\left(\frac{2}{x+2}-\frac{4}{x^2+4x+4}\right):\left(\frac{2}{x^2-4}+\frac{1}{2-x}\right)\)
\(=\left[\frac{2}{x+2}-\frac{4}{\left(x+2\right)^2}\right]:\left[\frac{2}{\left(x-2\right)\left(x+2\right)}+\frac{-1}{x-2}\right]\)
\(=\left[\frac{2\left(x+2\right)}{\left(x+2\right)^2}-\frac{4}{\left(x+2\right)^2}\right]:\left[\frac{2}{\left(x-2\right)\left(x+2\right)}+\frac{-\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\right]\)
\(=\frac{2\left(x+2\right)-4}{\left(x+2\right)^2}:\frac{2-\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)\(=\frac{2x+4-4}{\left(x+2\right)^2}:\frac{2-x-2}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{2x}{\left(x+2\right)^2}:\frac{-x}{\left(x-2\right)\left(x+2\right)}=\frac{2x}{\left(x+2\right)^2}.\frac{-\left(x-2\right)\left(x+2\right)}{x}\)
\(=\frac{-2\left(x-2\right)}{x+2}\)
BA
20 tháng 2 2020
\(\left(\frac{2}{x+2}-\frac{4}{x^2+4x+4}\right):\left(\frac{2}{x^2-4}+\frac{1}{2-x}\right)\)
\(\Leftrightarrow\left(\frac{2}{x+2}-\frac{4}{\left(x+2\right)^2}\right):\left(\frac{2}{\left(x-2\right)\left(x+2\right)}+\frac{1}{2-x}\right)\)
\(\Leftrightarrow\frac{2x+4-4}{\left(x+2\right)^2}:\frac{2+x+2}{\left(x-2\right)\left(x+2\right)}\)
\(\Leftrightarrow\frac{2x}{\left(x+2\right)^2}\cdot\frac{\left(x-2\right)\left(x+2\right)}{x+4}\)
\(\Leftrightarrow\frac{2x^2-4x}{\left(x+2\right)\left(x+4\right)}\)
BP
6 tháng 1 2020
a) \(\left(3-2x\right)\left(x+1\right)+x\left(2x-1\right)=3x+3-2x^2-2x+2x^2-x=3\)
b) \(\frac{x^2+9}{x^2+3x}+\frac{6}{x+3}=\frac{x^2+9}{x\left(x+3\right)}+\frac{6x}{x\left(x+3\right)}=\frac{x^2+6x+9}{x\left(x+3\right)}=\frac{\left(x+3\right)^2}{x\left(x+3\right)}=\frac{x+3}{x}\)
c)\(\frac{2+x}{2-x}+\frac{4x^2}{4-x^2}+\frac{x-2}{2+x}=\frac{\left(x+2\right)^2}{\left(2-x\right)\left(2+x\right)}+\frac{4x^2}{\left(2-x\right)\left(2+x\right)}+\frac{-\left(x-2\right)^2}{\left(2+x\right)\left(2-x\right)}\)
\(=\frac{x^2+4x+4+4x^2-x^2+4x-4}{\left(2-x\right)\left(2+x\right)}=\frac{4x^2+8x}{\left(x+2\right)\left(2-x\right)}=\frac{4x\left(x+2\right)}{\left(x+2\right)\left(2-x\right)}=\frac{4x}{2-x}\)
d) \(\left(x^3+4x^2+6x+4\right):\left(x+2\right)\)
\(=\left(x^3+2x^2+2x^2+4x+2x+4\right):\left(x+2\right)\)
\(=\left[x^2\left(x+2\right)+2x\left(x+2\right)+2\left(x+2\right)\right]:\left(x+2\right)\)
\(=\left(x^2+2x+2\right)\left(x+2\right):\left(x+2\right)=x^2+2x+2\)
16 tháng 11 2017
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NV
Nguyễn Việt Lâm
Giáo viên
20 tháng 4 2019
a/ \(\left(2n^3-5n^2+1\right):\left(2n-1\right)=n^2-2n-1\)
b/ \(x\ne0;\pm2\)
\(\left(\frac{x^2}{x\left(x^2-4\right)}-\frac{6}{3\left(x-2\right)}+\frac{1}{x+2}\right):\left(\frac{x^2-4+10-x^2}{x+2}\right)\)
\(=\left(\frac{x}{x^2-4}-\frac{2\left(x+2\right)}{x^2-4}+\frac{x-2}{x^2-4}\right):\left(\frac{6}{x+2}\right)\)
\(=\left(\frac{x-2x-4+x-2}{\left(x-2\right)\left(x+2\right)}\right).\left(\frac{x+2}{6}\right)\)
\(=\frac{-6}{\left(x-2\right)\left(x+2\right)}.\frac{\left(x+2\right)}{6}=-\frac{1}{x-2}=\frac{1}{2-x}\)
c/
\(\left(3x-1\right)^2+2\left(3x-1\right)\left(3x+4\right)+\left(3x+4\right)^2\)
\(=\left(3x-1+3x+4\right)^2\)
\(=\left(6x+3\right)^2\)
Answer:
\(\frac{x+2}{x-3}+\frac{x^2+6}{x^2-3x}\left(ĐK:x\ne0;x\ne3\right)\)
\(=\frac{x+2}{x-3}+\frac{x^2+6}{x\left(x-3\right)}\)
\(=\frac{x\left(x+2\right)+x^2+6}{x\left(x-3\right)}\)
\(=\frac{x^2+2x+x^2+6}{x\left(x-3\right)}\)
\(=\frac{2x^2+2x+6}{x\left(x-3\right)}\)
\(\frac{4x-4}{x^2-4x+4}:\frac{x^2-1}{\left(2-x\right)^2}\left(ĐK:x\ne2;x\ne\pm1\right)\)
\(=\frac{4\left(x-1\right)}{\left(x-2\right)^2}.\frac{\left(2-x\right)^2}{x^2-1}\)
\(=\frac{4\left(x-1\right)}{\left(x-2\right)^2}.\frac{\left(x-2\right)^2}{\left(x-1\right)\left(x+1\right)}\)
\(=\frac{4}{x+1}\)