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\(\dfrac{x^2-2x-8}{2x^2+9x+10}\)
\(=\dfrac{x^2-4x+2x-8}{2x^2+4x+5x+10}\)
\(=\dfrac{\left(x-4\right)\left(x+2\right)}{\left(x+2\right)\left(2x+5\right)}\)
\(=\dfrac{x-4}{2x+5}\)
\(\left(x-2\right)^3+\left(2x+1\right)^2+2\left(x+2\right)\left(1-x\right)-9x^3+2x\)
\(=x^3-6x^2+12x-8+8x^3+12x^2+6x+1+2\left(x+2\right)\left(1-x\right)-9x^3+2x\)
\(=9x^3+6x^2+18x-7+2\left(x-x^2+2-2x\right)-9x^3+2x\)
\(=6x^2+20x-7-2x^2-2x+4=4x^2+18x-3\)
a kham khảo nha , e nhờ a e lm chứ ko phải e lm nha !
\(\left(x-2\right)\left(\frac{3}{x}+2-\frac{5}{2x}-4+\frac{8}{x^2}-4\right)\)
\(\left(x-2\right)\left[\left(\frac{3}{x}-\frac{5}{2x}\right)-6+\frac{8}{x^2}\right]\)
\(\left(x-2\right)\left(\frac{1}{2x}-6+\frac{8}{x^2}\right)\)
\(\left(x-2\right)\left(\frac{3}{x+2}-\frac{5}{2x-4}+\frac{8}{x^2-4}\right)\)
\(=\left(x-2\right)\left[\frac{3}{x+2}-\frac{5}{2\left(x-2\right)}+\frac{8}{\left(x-2\right)\left(x+2\right)}\right]\)
\(=\left(x-2\right)\left[\frac{3.2\left(x-2\right)}{2\left(x-2\right)\left(x+2\right)}-\frac{5\left(x+2\right)}{2\left(x-2\right)\left(x+2\right)}+\frac{8.2}{2\left(x-2\right)\left(x+2\right)}\right]\)
\(=\left(x-2\right)\left[\frac{6\left(x-2\right)}{2\left(x-2\right)\left(x+2\right)}-\frac{5\left(x+2\right)}{2\left(x-2\right)\left(x+2\right)}+\frac{16}{2\left(x-2\right)\left(x+2\right)}\right]\)
\(=\left(x-2\right)\left[\frac{6\left(x-2\right)-5\left(x+2\right)+16}{2\left(x-2\right)\left(x+2\right)}\right]\)
\(=\frac{\left(x-2\right)\left(x-6\right)}{2\left(x-2\right)\left(x+2\right)}\)
\(=\frac{x-6}{2\left(x+2\right)}\)
Các bạn giúp mình với nhé thanks
\(\dfrac{x^2-2x-8}{2x^2+9x+10}\)
\(=\dfrac{\left(x-4\right)\left(x+2\right)}{2x^2+4x+5x+10}\)
\(=\dfrac{\left(x-4\right)\left(x+2\right)}{\left(x+2\right)\left(2x+5\right)}\)
\(=\dfrac{x-4}{2x+5}\)