Rút gọn phân thức sau x-2/2x-x^2
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BT
2
15 tháng 3 2020
a kham khảo nha , e nhờ a e lm chứ ko phải e lm nha !
\(\left(x-2\right)\left(\frac{3}{x}+2-\frac{5}{2x}-4+\frac{8}{x^2}-4\right)\)
\(\left(x-2\right)\left[\left(\frac{3}{x}-\frac{5}{2x}\right)-6+\frac{8}{x^2}\right]\)
\(\left(x-2\right)\left(\frac{1}{2x}-6+\frac{8}{x^2}\right)\)
15 tháng 3 2020
\(\left(x-2\right)\left(\frac{3}{x+2}-\frac{5}{2x-4}+\frac{8}{x^2-4}\right)\)
\(=\left(x-2\right)\left[\frac{3}{x+2}-\frac{5}{2\left(x-2\right)}+\frac{8}{\left(x-2\right)\left(x+2\right)}\right]\)
\(=\left(x-2\right)\left[\frac{3.2\left(x-2\right)}{2\left(x-2\right)\left(x+2\right)}-\frac{5\left(x+2\right)}{2\left(x-2\right)\left(x+2\right)}+\frac{8.2}{2\left(x-2\right)\left(x+2\right)}\right]\)
\(=\left(x-2\right)\left[\frac{6\left(x-2\right)}{2\left(x-2\right)\left(x+2\right)}-\frac{5\left(x+2\right)}{2\left(x-2\right)\left(x+2\right)}+\frac{16}{2\left(x-2\right)\left(x+2\right)}\right]\)
\(=\left(x-2\right)\left[\frac{6\left(x-2\right)-5\left(x+2\right)+16}{2\left(x-2\right)\left(x+2\right)}\right]\)
\(=\frac{\left(x-2\right)\left(x-6\right)}{2\left(x-2\right)\left(x+2\right)}\)
\(=\frac{x-6}{2\left(x+2\right)}\)
VN
1
16 tháng 12 2021
\(x^3+2x^2-x-2\)
\(=x^3+3x^2+2x-1x^2-3x-2\)
\(=x\left(x^2+3x+2\right)-1\left(x^2+3x+2\right)\)
\(=\left(x-1\right)\left(x^2+3x+2\right)\)
\(=\left(x-1\right)\left(x^2+x+2x+2\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x+2\right)\)
\(x^3+3x+2\)
\(=x^3+2x^2-2x^2-4x+x+2\)
\(=\left(x+2\right)x^2-2\left(x^2+2x\right)+x+2\)
\(=\left(x+2\right)x^2-2\left(x^2+2x\right)1\left(x+2\right)\)
\(=\left(x^2-2x+1\right)\left(x+2\right)\)
\(=\left(x-1\right)^2\left(x+2\right)\)
TT
1
25 tháng 7 2023
a: \(=\dfrac{3\left(x-2\right)}{\left(x-2\right)^3}=\dfrac{3}{\left(x-2\right)^2}\)
b: \(=\dfrac{x^2\left(x+2\right)}{\left(x+2\right)^3}=\dfrac{x^2}{\left(x+2\right)^2}\)
PT
0
TK
1
17 tháng 8 2021
\(\dfrac{x^2-2x-8}{2x^2+9x+10}\)
\(=\dfrac{x^2-4x+2x-8}{2x^2+4x+5x+10}\)
\(=\dfrac{\left(x-4\right)\left(x+2\right)}{\left(x+2\right)\left(2x+5\right)}\)
\(=\dfrac{x-4}{2x+5}\)
TK
2
17 tháng 8 2021
\(\dfrac{x^2-2x-8}{2x^2+9x+10}\)
\(=\dfrac{\left(x-4\right)\left(x+2\right)}{2x^2+4x+5x+10}\)
\(=\dfrac{\left(x-4\right)\left(x+2\right)}{\left(x+2\right)\left(2x+5\right)}\)
\(=\dfrac{x-4}{2x+5}\)
HK
1
15 tháng 8 2016
\(\frac{x^4+x^3+x+1}{x^4-x^3+2x^2-x+1}\)
\(=\frac{x\left(x+1\right)+\left(x+1\right)}{x\left(x-1\right)+2x^2-2x+x+1}\)
\(=\frac{\left(x+1\right)\left(x+1\right)}{x\left(x-1\right)+2\left(x-1\right)+\left(x+1\right)}\)
Ddeeff sao rồi bạn ko rút gọn được
SC
1
14 tháng 2 2020
\(\frac{2x^2-3x-20}{x^2-16}\)
\(=\frac{2x^2-8x+5x-20}{\left(x-4\right)\left(x+4\right)}\)
\(=\frac{2x\left(x-4\right)+5\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}\)
\(=\frac{\left(2x+5\right)\left(x-4\right)}{\left(x+4\right)\left(x-4\right)}\)
\(=\frac{2x+5}{x+4}\)
Vậy ...
TL
\(\frac{x-2}{2x-x^2}\)=\(-\frac{2-x}{x.\left(2-x\right)}\)=\(-\frac{1}{x}\)
HỌC TỐT
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