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a: \(=x^2-36-x^2-14x-49+14x=-85\)
b: \(=\dfrac{5x+35+4x-28-5x-7}{\left(x-7\right)\left(x+7\right)}=\dfrac{4x}{x^2-49}\)
\(a,\left(x+6\right)\left(x-6\right)-\left(x+7\right)^2+14x=x^2-36-x^2-14x-49+14x=-85\\ b,\dfrac{5}{x-7}+\dfrac{4}{x+7}+\dfrac{5x+7}{49-x^2}=\dfrac{5\left(x+7\right)+4\left(x-7\right)-\left(5x+7\right)}{\left(x-7\right)\left(x+7\right)}=\dfrac{5x+35+4x-28-5x-7}{\left(x-7\right)\left(x+7\right)}=\dfrac{4x}{\left(x-7\right)\left(x+7\right)}\)
a)=\(3x^3-15x^2+21x\)
b)\(=-2x^4y-10x^2y+2xy\)
c)\(=-x^3+6x^2+5x-4x^2+24x+20=-x^3+2x^2+29x+20\)
d)\(=2x^4-3x^3+4x^2-2x^2+3x-4=2x^4-3x^32x^2+3x-4\)
e)\(=x^2-4y^2\)
f)\(=-2x^2y^3+y-3\)
g)\(=3xy^4-\dfrac{1}{2}y^2+2x^2y\)
h)\(=9x^2-6x+1-7x^2-14=2x^2-6x-13\)
i)\(=x^2-x-3\)
j)\(=\left(x+2y\right)\left(x^2-2y+4y^2\right):\left(x+2y\right)=x^2-2y+4y^2\)
a: \(=\dfrac{2\left(x+2\right)\left(x-1\right)}{x+2}=2x-2\)
b: \(=\dfrac{2x^3+x^2-6x^2-3x+2x+1}{2x+1}=x^2-3x+1\)
c: \(=\dfrac{x^3+2x^2-2x^2-4x+2x+4}{x+2}=x^2-2x+2\)
d: \(=\dfrac{x^2\left(x-3\right)}{x-3}=x^2\)
Bài 1:
a, (\(x\) - 4).(\(x\) + 4) - (5 - \(x\)).(\(x\) + 1)
= \(x^2\) - 16 - 5\(x\) - 5 + \(x^2\) + \(x\)
= (\(x^2\) + \(x^2\)) - (5\(x\) - \(x\)) - (16 + 5)
= 2\(x^2\) - 4\(x\) - 21
b, (3\(x^2\) - 2\(xy\) + 4) + (5\(xy\) - 6\(x^2\) - 7)
= 3\(x^2\) - 2\(xy\) + 4 + 5\(xy\) - 6\(x^2\) - 7
= (3\(x^2\) - 6\(x^2\)) + (5\(xy\) - 2\(xy\)) - (7 - 4)
= - 3\(x^2\) + 3\(xy\) - 3
b: \(\dfrac{4}{x+2}+\dfrac{2}{x-2}+\dfrac{5-6x}{4-x^2}\)
\(=\dfrac{4x-8+2x+4+6x-5}{\left(x-2\right)\left(x+2\right)}=\dfrac{12x-9}{\left(x-2\right)\left(x+2\right)}\)
c: \(\dfrac{x^3+2x}{x^3+1}+\dfrac{2x}{x^2-x+1}+\dfrac{1}{x+1}\)
\(=\dfrac{x^3+2x+2x^2+2x+x^2-x+1}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{x^3+3x^2+3x+1}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{\left(x+1\right)^3}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{x^2+2x+1}{x^2-x+1}\)
e: \(\dfrac{7}{x}-\dfrac{x}{x+6}+\dfrac{36}{x^2+6x}\)
\(=\dfrac{7x+42-x^2+36}{x\left(x+6\right)}\)
\(=\dfrac{-x^2+7x+78}{x\left(x+6\right)}\)
\(=\dfrac{-x^2+13x-6x+78}{x\left(x+6\right)}\)
\(=\dfrac{-x\left(x-13\right)-6\left(x-13\right)}{x\left(x+6\right)}\)
\(=\dfrac{\left(13-x\right)\left(x+6\right)}{x\left(x+6\right)}=\dfrac{13-x}{x}\)
\(=\left[\left(-6x\right)+\left(x^2+9\right)\right]\left[\left(-6x\right)-\left(x^2+9\right)\right]\)
\(=\left(-6x\right)^2-\left(x^2+9\right)^2\)
\(=36x^2-\left(x^4+18x^2+81\right)\)
\(=-x^4+18x^2-81\)
\(=-\left(x^4-18x^2+81\right)\)
\(=-\left(x^2-9\right)^2\)
Ta có: \(\left(x^2-6x+9\right)\left(-x^2-6x-9\right)\)
\(=-\left(x^2-6x+9\right)\left(x^2+6x+9\right)\)
\(=-\left[\left(x-3\right)^2\cdot\left(x+3\right)^2\right]\)
\(=-\left(x^2-9\right)^2\)
a: \(\left(x+5\right)\left(x+1\right)-x^2\)
\(=x^2+6x+5-x^2\)
=6x+5