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27 tháng 7 2016

\(\left(x^2-9\right)^2-\left(x+3\right)\left(x-3\right)\left(x^2+9\right)=\left(x-3\right)^2\left(x+3\right)^2-\left(x+3\right)\left(x-3\right)\left(x^2+9\right)\)

\(=\left(x-3\right)\left(x+3\right)\left[\left(x-3\right)\left(x+3\right)-x^2+9\right]=\left(x-3\right)\left(x+3\right)\left[x^2-9-x^2-9\right]=\left(x-3\right)\left(x+3\right)\cdot\left(-18\right)\)

\(=-18\left(x+3\right)\left(x-3\right)\)

27 tháng 12 2021

\(=\dfrac{-x^2-2x+3+x^2+x}{\left(x-3\right)\left(x+3\right)}=\dfrac{-x+3}{\left(x-3\right)\left(x+3\right)}=\dfrac{-1}{x+3}\)

6 tháng 8 2020

cau hoi nay de lam ma

6 tháng 8 2020

\(\frac{4}{x-3}+\frac{5}{x+3}-\frac{13-9x^2}{x^2-9}\)

ĐKXĐ : \(x\ne\pm3\)

\(=\frac{4}{x-3}+\frac{5}{x+3}-\frac{13-9x^2}{\left(x+3\right)\left(x-3\right)}\)

\(=\frac{4\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}+\frac{5\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}-\frac{13-9x^2}{\left(x+3\right)\left(x-3\right)}\)

\(=\frac{4x+12}{\left(x+3\right)\left(x-3\right)}+\frac{5x-15}{\left(x+3\right)\left(x-3\right)}-\frac{13-9x^2}{\left(x+3\right)\left(x-3\right)}\)

\(=\frac{4x+12+5x-15-13+9x^2}{\left(x+3\right)\left(x-3\right)}\)

\(=\frac{9x^2+9x-16}{\left(x+3\right)\left(x-3\right)}=\frac{9x^2+9x-16}{x^2-9}\)

27 tháng 7 2016

\(\left(x^2-9\right)^2-\left(x+3\right)\left(x-3\right)\left(x^2+9\right)=x^4-18x^2+81-\left(x^2-9\right)\left(x^2+9\right)=x^4-18x^2+81-\left(x^4-81\right)=x^4-18x^2+81-x^4+81=-18x^2+162=-18\left(x^2-9\right)=-18\left(x-3\right)\left(x+3\right)\)

8 tháng 8 2020

\(\left(x-2\right)\left(x^2+2x+4\right)-\left(x-1\right)^3+7\)

\(=x^3-8-\left(x^3-3x^2+3x-1\right)+7\)

\(=x^3-8+7-x^3+3x^2-3x+1\)

\(=\left(x^3-x^3\right)+\left(7+1-8\right)+3x^2-3x\)

\(=3x^2-3x=3x\left(x-1\right)\)

8 tháng 8 2020

\(x\left(x+2\right)\left(2-x\right)+\left(x+3\right)\left(x^2-3x+9\right)\)

\(=x\left(2+x\right)\left(2-x\right)+\left(x+3\right)\left(x^2-3x+9\right)\)

\(=x\left(4-x^2\right)+\left(x+3\right)\left(x^2-3x+9\right)\)

\(=4x-x^3+\left(x^3+9\right)\)

\(=4x-\left(x^3-x^3\right)+9\)

\(=4x+9\)

12 tháng 3 2020

\(\frac{6}{x^2-9}+\frac{5x}{x-3}+\frac{x}{x+3}\)

\(=\frac{6x}{\left(x-3\right)\left(x+3\right)}+\frac{5x}{x-3}+\frac{x}{x+3}\)

\(=\frac{6x}{\left(x-3\right)\left(x+3\right)}-\frac{5x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{6x+5x\left(x+3\right)+x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{6x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\frac{6x}{x-3}\)

12 tháng 3 2020

\(\frac{6x}{x^2-9}+\frac{5x}{x-3}+\frac{x}{x+3}\left(x\ne\pm3\right)\)

\(=\frac{6x}{\left(x-3\right)\left(x+3\right)}+\frac{5x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{6x+5x^2+15x+x^2-3x}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{6x^2+18x}{\left(x-3\right)\left(x+3\right)}=\frac{6x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\frac{6x}{x-3}\)

23 tháng 12 2021

a: \(=x^2+2x-8-x^2-2x-1=-9\)

b: \(=\dfrac{x^2+6x+9+3x-9+2x^2-18x}{x\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{3x^2-9x}{x\left(x-3\right)\left(x+3\right)}=\dfrac{3x\left(x-3\right)}{x\left(x-3\right)\left(x+3\right)}=\dfrac{3}{x+3}\)

21 tháng 8 2023

a) \(\dfrac{2x}{x^2-6x+9}+\dfrac{x-2}{x-3}\) (ĐK: \(x\ne3\))

\(=\dfrac{2x}{\left(x-3\right)^2}+\dfrac{x-2}{x-3}\)

\(=\dfrac{2x}{\left(x-3\right)^2}+\dfrac{\left(x-2\right)\left(x-3\right)}{\left(x-3\right)^2}\)

\(=\dfrac{2x+x^2-2x-3x+6}{\left(x-3\right)^2}\)

\(=\dfrac{x^2-3x+6}{x^2-6x+9}\)

b) \(\dfrac{x^2+2}{x^3-1}+\dfrac{2}{x^2+x+1}-\dfrac{1}{x-1}\)

\(=\dfrac{x^2+2}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{2\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}-\dfrac{x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}\)

\(=\dfrac{x^2+2+2x-2-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}\)

\(=\dfrac{x-1}{\left(x-1\right)\left(x^2+x+1\right)}\)

\(=\dfrac{1}{x^2+x+1}\)