rút gọn x^2+4x-5/x^2-4x+3:x^2+10x+25/x^2-x-6
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15 tháng 10 2021
a: \(\dfrac{x^3-x}{3x+3}=\dfrac{x\left(x-1\right)\left(x+1\right)}{3\left(x+1\right)}=\dfrac{x\left(x-1\right)}{3}\)
b: \(\dfrac{x^2-4xy+4y^2-4}{2x^2-4xy+4x}\)
\(=\dfrac{\left(x-2y\right)^2-4}{2x\left(x-2y+2\right)}\)
\(=\dfrac{x-2y-2}{2x}\)
DT
1
5 tháng 2 2022
\(=\dfrac{\left(x+3\right)\left(x-1\right)}{\left(x+5\right)\left(x-2\right)}\cdot\dfrac{\left(x-2\right)\left(x-7\right)}{\left(x+3\right)\left(x-2\right)}:\dfrac{\left(x-1\right)\left(x-3\right)}{\left(x+2\right)\left(x+5\right)}\)
\(=\dfrac{\left(x-1\right)\left(x-7\right)}{\left(x+5\right)\left(x-2\right)}\cdot\dfrac{\left(x+2\right)\left(x+5\right)}{\left(x-1\right)\left(x-3\right)}=\dfrac{\left(x-7\right)\left(x+2\right)}{\left(x-2\right)\left(x-3\right)}\)
27 tháng 7 2022
Bài 1:
\(D=-3x^2+x+15x-5-3\left(2x^2-5x+2\right)\)
\(=-3x^2+16x-5-6x^2+15x-6\)
\(=-9x^2+31x-11\)
\(=-9\cdot\dfrac{1}{9}+\dfrac{31}{3}-11\)
=-11-1+31/3=-12+31/3=-5/3
b: \(E=x^2+x-56-x^2+7x-10=8x-66\)
\(=-\dfrac{8}{5}-66=-\dfrac{338}{5}\)
c: \(F=-3\left(2x^2+x-16x-8\right)-\left(-3x^2+2x-15x+10\right)-4x^2+24x\)
\(=-6x^2+45x+24+3x^2+13x-10-4x^2+24x\)
\(=-4x^2+82x+14\)
\(=-4\cdot9-82\cdot3+14=-268\)
26 tháng 10 2021
1) ĐKXĐ: \(x\ge\dfrac{5}{2}\)
\(\sqrt{x^2}=2x-5\\ \Rightarrow\left|x\right|=2x-5\\ \Rightarrow\left[{}\begin{matrix}x=2x-5\\x=5-2x\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\left(tm\right)\\x=\dfrac{5}{3}\left(ktm\right)\end{matrix}\right.\)
2) ĐKXĐ: \(x\ge3\)
\(\sqrt{25x^2-10x+1}=2x-6\\ \Rightarrow\left|5x-1\right|=2x-6\\ \Rightarrow\left[{}\begin{matrix}5x-1=2x-6\\5x-1=6-2x\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{5}{3}\left(ktm\right)\\x=1\left(tm\right)\end{matrix}\right.\)
3) ĐKXĐ: \(x\ge\dfrac{5}{2}\)
\(\sqrt{25-10x+x^2}=2x-5\\ \Rightarrow\left|x-5\right|=2x-5\\ \Rightarrow\left[{}\begin{matrix}x-5=2x-5\\x-5=5-2x\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x=\dfrac{10}{3}\left(tm\right)\end{matrix}\right.\)
4) ĐKXĐ: \(x\ge\dfrac{1}{2}\)
\(\sqrt{1-2x+x^2}=2x-1\\ \Rightarrow\left|x-1\right|=2x-1\\ \Rightarrow\left[{}\begin{matrix}x-1=2x-1\\x-1=1-2x\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x=\dfrac{2}{3}\left(tm\right)\end{matrix}\right.\)
15 tháng 7 2022
Bài 1:
8: \(=\dfrac{x+3}{x\left(x-3\right)}\)
9: \(=\dfrac{x-2}{x-5}\cdot\dfrac{\left(x-5\right)\left(x+5\right)}{\left(x-2\right)^2}=\dfrac{x+5}{x-2}\)
10: \(=1:\dfrac{a-1}{a}=\dfrac{a}{a-1}\)
12: \(=\dfrac{6\left(x+1\right)}{3x\left(x+1\right)}=\dfrac{2}{x}\)
13: \(\dfrac{3}{x+3}-\dfrac{x-6}{x\left(x+3\right)}\)
\(=\dfrac{3x-x+6}{x\left(x+3\right)}=\dfrac{2x+6}{x\left(x+3\right)}=\dfrac{2}{x}\)
DL
3
TG
18 tháng 7 2021
Em bấm vào biểu tượng \(\sum\) trên thanh công cụ và gõ phân số để mn dễ hỗ trợ nhé!
18 tháng 7 2021
`(x^2+x-6)/(x^2+4x+3):(x^2-10x+25)/(x^2-4x-5)(x ne -1,x ne 5,x ne -3)`
`=((x-2)(x+3))/((x+1)(x+3)):(x-5)^2/((x+1)(x-5))`
`=(x-2)/(x+1):(x-5)/(x+1)`
`=(x-2)/(x-5)`
PA
21 tháng 10 2016
\(\frac{2+x}{2-x}\div\frac{4x^2}{4-4x+x^2}\times\left(\frac{2}{2-x}-\frac{8}{8+x^3}\times\frac{4-2x+x^2}{2-x}\right)\)
\(=\frac{2+x}{2-x}\times\frac{4-4x+x^2}{4x^2}\times\left(\frac{2}{2-x}-\frac{8}{\left(2+x\right)\left(4-2x+x^2\right)}\times\frac{4-2x+x^2}{2-x}\right)\)
\(=\frac{2+x}{2-x}\times\frac{\left(2-x\right)^2}{4x^2}\times\left(\frac{2\left(2+x\right)}{\left(2+x\right)\left(2+x\right)}-\frac{8}{\left(2+x\right)\left(2-x\right)}\right)\)
\(=\frac{\left(2+x\right)\left(2-x\right)}{4x^2}\times\frac{4+2x-8}{\left(2+x\right)\left(2-x\right)}\)
\(=\frac{2\left(2+x-4\right)}{4x^2}\)
\(=\frac{x-2}{2x^2}\)