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\(\left(x^2+6x+15\right)\left(x^2+10x+21\right)+15=\left(x+5\right)\left(x+1\right)\left(x+3\right)\left(x+7\right)+15=\left(x+5\right)\left(x+3\right)\left(x+1\right)\left(x+7\right)+15=\left(x^2+8x+15\right)\left(x^2+8x+7\right)+15\)
Đặt \(x^2+8x+7=a\)
Khi đó pt thành \(a\left(a+8\right)+15=a^2+8a+15=\left(a+3\right)\left(a+5\right)\)
Do đó: \(\left(x^2+6x+5\right)\left(x^2+10x+21\right)+15=\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{3x}{5x+5y}-\frac{x}{10x-10y}\)
= \(\frac{3x\left(x-y\right)}{5.2.\left(x+y\right)\left(x-y\right)}-\frac{x\left(x+y\right)}{10\left(x^2-y^2\right)}\)
= \(\frac{3x^2-3xy-x^2-xy}{10\left(x^2-y^2\right)}\)
= \(\frac{3x\left(x-y\right)}{10\left(x^2-y^2\right)}\)
= \(\frac{3x}{10\left(x+y\right)}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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Bài 1:
a) \(\dfrac{15xy}{10x^2y}\)
= \(\dfrac{3.5xy}{2.5xyx}\)
= \(\dfrac{3}{2x}\)
d) \(\dfrac{6x\left(x+5\right)^3}{2x^2\left(x+5\right)}\)
= \(\dfrac{3.2x\left(x+5\right)\left(x+5\right)^2}{x.2x\left(x+5\right)}\)
= \(\dfrac{3\left(x+5\right)^2}{x}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(x^2\left(1-3x\right)-6x+2=0\)
\(\Rightarrow x^2\left(1-3x\right)+2\left(1-3x\right)=0\)
\(\Rightarrow\left(x^2+2\right)\left(1-3x\right)=0\)
\(\Rightarrow1-3x=0\) (x2 + 2 loại)
\(\Rightarrow x=\dfrac{1}{3}\)
b) \(\left(2x-3\right)x^2=15-10x\)
\(\Rightarrow2x^3-3x^2+10x-15=0\)
Rồi lấy máy tính nhấn nghiệm nhé, mk ko có máy tính.
\(A=\left(x^2+6x+5\right)\left(x^2+10x+21\right)+15\)
\(=\left[x\left(x+1\right)+5\left(x+1\right)\right].\left[x\left(x+3\right)+7\left(x+3\right)\right]+15\)
\(=\left(x+1\right)\left(x+5\right)\left(x+3\right)\left(x+7\right)+15\)
\(=\left[\left(x+1\right)\left(x+7\right)\right].\left[\left(x+3\right)\left(x+5\right)\right]+15\)
\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)
Đặt \(x^2+8x+11=a\)
Ta có:
\(A=\left(a-4\right)\left(a+4\right)+15\)
\(=a^2-1=\left(a-1\right)\left(a+1\right)\)
\(=\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)
\(=\left(x^2+8x+10\right)\left[x\left(x+2\right)+6\left(x+2\right)\right]=\left(x^2+8x+10\right)\left(x+2\right)\left(x+6\right)\)
Chúc bạn học tốt.