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(x+5)2+(x-2)2-4(x-3)(x+3)
=x2+10x+25+x2-4x+4-4x2+36
=x2+x2-4x2+10x-4x+25+4+36
=-2x2+6x+65
\(\frac{4}{x-3}+\frac{5}{x+3}-\frac{13-9x^2}{x^2-9}\)
ĐKXĐ : \(x\ne\pm3\)
\(=\frac{4}{x-3}+\frac{5}{x+3}-\frac{13-9x^2}{\left(x+3\right)\left(x-3\right)}\)
\(=\frac{4\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}+\frac{5\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}-\frac{13-9x^2}{\left(x+3\right)\left(x-3\right)}\)
\(=\frac{4x+12}{\left(x+3\right)\left(x-3\right)}+\frac{5x-15}{\left(x+3\right)\left(x-3\right)}-\frac{13-9x^2}{\left(x+3\right)\left(x-3\right)}\)
\(=\frac{4x+12+5x-15-13+9x^2}{\left(x+3\right)\left(x-3\right)}\)
\(=\frac{9x^2+9x-16}{\left(x+3\right)\left(x-3\right)}=\frac{9x^2+9x-16}{x^2-9}\)
2x^4 + 2x^3 + 3x^2 - 5x - 20 x^2 + x + 4 2x^2 - 5 2x^4 + 2x^3 + 8x^2 -5x^2 - 5x - 20 -5x^2 - 5x - 20 0
Vậy \(\left(2x^4+2x^3+3x^2-5x-20\right):\left(x^2+x+4\right)=2x^2-5\)
\(3x\left(x-1\right)^2-2x\left(x+3\right)\left(x-3\right)+4x\left(x-4\right)\)
\(=3x\left(x^2-2x+1\right)-2x\left(x^2-9\right)+4x^2-16x\)
\(=3x^3-6x^2+3x-2x^3+18x+4x^2-16x\)
\(=\left(3x^3-2x^3\right)+\left(4x^2-6x^2\right)+\left(3x-16x\right)\)
\(=x^3-2x^2-13x\)
\(\frac{4}{x+2}+\frac{3}{x-2}+\frac{-5x-2}{x^2-4}\)ĐK : \(x\ne\pm2\)
\(=\frac{4\left(x-2\right)+3\left(x+2\right)-5x-2}{\left(x+2\right)\left(x-2\right)}=\frac{4x-8+3x+6-5x-2}{\left(x+2\right)\left(x-2\right)}\)
\(=\frac{2x-4}{\left(x+2\right)\left(x-2\right)}=\frac{2\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}=\frac{2}{x+2}\)
a, \(\left(2x^3-x^2+5x\right):x=2x^2-x+5\)
b, \(\left(3x^4-2x^3+x^2\right):\left(-2x\right)=-\frac{3}{2}x^3+x^2-\frac{1}{2}x\)
\(\left(2x^3-x^2+5x\right):5=\left(2x^3:x\right)+\left(-x^2:x\right)+\left(5x:x\right)=2x^2-x+5\)
\(\left(3x^4-2x^3+x^2\right):\left(-2x\right)=[3x^4:\left(-2x\right)]+[-2x^3:\left(-2x\right)]+[x^2:\left(-2x\right)]=-\frac{3}{2}x^3+x^2-\frac{x}{2}\)
theo cách tính tổng (bn có thể xem lại ở toán 7 hay 6 j đấy) thì bt trên bằng 1/x - 1/(x+5)
từ đó tính tiếp nha bn
`@` `\text {Ans}`
`\downarrow`
`(x+3)(x-4)`
`= x(x-4) + 3(x-4)`
`= x^2-4x + 3x - 12`
`= x^2 - x - 12`
=x^2-4x+3x-12
=x^2-x-12