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\(a)=\frac{-2\left(x+3\right)}{x\left(1-3x\right)}.\frac{1-3x}{x\left(x+3\right)}\)
\(=\frac{-2}{x^2}\)
\(b)=\frac{\left(x+3\right)\left(x-3\right)}{x\left(x-3\right)}-\frac{x^2}{x\left(x-3\right)}+\frac{9}{x\left(x-3\right)}\)
\(=\frac{x^2-3x+3x-9-x^2+9}{x\left(x-3\right)}\)
\(=x\left(x-3\right)\)
\(c)=\frac{x+3}{\left(x-1\right)\left(x+1\right)}-\frac{1}{x\left(x+1\right)}\)
\(=\frac{\left(x+3\right).x}{x\left(x-1\right)\left(x+1\right)}-\frac{1.\left(x-1\right)}{x\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x^2+3x-x+1}{x\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x\left(x+3\right)-\left(x-1\right)}{x\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x+3}{x+1}\)
# Sắp ik ngủ nên làm vậy hoi, ko chắc phần kq câu b và c đâu nha
bài 1.
a.\(\left(x+4\right)\left(x^2-4x+16\right)=x^3-4^3=x^3-64\)
b.\(\left(x^2-\frac{1}{3}\right)\left(x^4+\frac{1}{3}x^2+\frac{1}{9}\right)=\left(x^2\right)^3-\left(\frac{1}{3}\right)^3=x^6-\frac{1}{27}\)
bài 2.
a.\(892^2+892.216+108^2=892^2+2.892.108+108^2\)
\(=\left(892+108\right)^2=1000^2=1_{ }000_{ }000\)
b.\(36^2+26^2-52.36=36^2+26^2-2.26.36=\left(36-26\right)^2=10^2=100\)
a) \(\frac{3x}{2x+4}+\frac{x+3}{x^2-4}\)
\(=\frac{3x}{2\left(x+2\right)}+\frac{x+3}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{3x\left(x-2\right)}{2\left(x+2\right)\left(x-2\right)}+\frac{2\left(x+3\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{3x\left(x-2\right)+2\left(x+3\right)}{2\left(x+2\right)\left(x-2\right)}\)
\(=\frac{3x^2-6x+2x+6}{2\left(x^2-4\right)}\)
\(=\frac{3x^2-4x+6}{2\left(x^2-4\right)}\)
a, \(\left(x+2\right)^9:\left(x+2\right)^6=\left(x+2\right)^3\)
b, mình xin lỗi nhưng đề có nhầm chỗ nào không thế :(
c, \(\left(x^2+2x+4\right)^5:\left(x^2+2x+4\right)=\left(x^2+2x+4\right)^4\)
d, \(2\left(x^2+1\right)^3:\dfrac{1}{3}\left(x^2+1\right)=6\left(x^2+1\right)^2\)
bài 3
a) (xy+1)2-(x-y)2
=[(xy+1)-(x-y)][(xy+1)+(x-y)]
=(xy+1-x+y)(xy+1+x-y)
b) x2-4y4+x+2y2
=(x2-4y4)+(x+2y2)
=(x-2y2)(x+2y2)+(x+2y2)
=(x+2y2)(x-2y2+1)
c) (x2+2x)2+9x2+18x
=(x2+2x)2+(9x2+18x)
=(x2+2x)2+9(x2+2x)
=(x2+2x)(x2+2x+9)
d) (x+2)(x+4)(x+6)(x+8)+16
=(x+2)(x+8) (x+4)(x+6) +16
=(x2+8x+2x+16)(x2+6x+4x+24)+16
=(x2+10x+16)(x2+10x+24)+16
đặt x2+10x+16=a ta có
a(a+8)+16
=a2+8a+16
=(a+4)2
thay a=(x2+10x+16) ta đc
(x2+10x+16)2
=(x2+8x+2x+16)2
=[x(x+8)+2(x+8)]2
=[ (x+2)(x+8)]2
Chọn đáp án A