1. \(\dfrac{x+1}{x-1}+\dfrac{3x}{x+1}=4\)
\(\Leftrightarrow\dfrac{\left(x+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}+\dfrac{3x\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}=\dfrac{4\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\)
\(\cdotĐKXĐ:x-1\ne0\Leftrightarrow x\ne1
\)
\(x+1\ne0\Leftrightarrow x\ne-1\)
pt: x2 + x + x + 1 +3x2 - 3x = 4x2 + 4x - 4x -4
\(\Leftrightarrow\) x2 + 3x2 - 4x2 + x + x - 3x + 4x - 4x = -4 -1
\(\Leftrightarrow\) - 1x = - 5
\(\Leftrightarrow\) x = \(\dfrac{-5}{-1}\)
\(\Leftrightarrow\) x = 5 ( nhận )
Vậy pt có tập nghiệm S= \(\left\{5\right\}\)
2. \(\left|x+2\right|< 2x+10\)
Vì x + 2 < 2x + 10(1) nên x + 2 > 0
-(x + 2) < 2x + 10(2) nên - (x + 2) <0
pt(1): x + 2 < 2x + 10
\(\Leftrightarrow\) x - 2x < 10 -2
\(\Leftrightarrow\) -x < 8
\(\Leftrightarrow\) x > -8 ( nhận )
pt(2): -(x + 2) < 2x + 10
\(\Leftrightarrow\) - x - 2 < 2x + 10
\(\Leftrightarrow\) - x - 2x < 10 + 2
\(\Leftrightarrow\) -3x < 12
\(\Leftrightarrow\) x < \(\dfrac{12}{-3}\)
\(\Leftrightarrow\) x < -4 ( nhận)
Vậy bpt có tập nghiệm S= \(\left\{x\left|x< -4\right|\right\}\)
\(\left\{x\left|x>-8\right|\right\}\)
Bài 1.
\(\dfrac{x+1}{x-1}+\dfrac{3x}{x+1}=4\)(đkxđ: x\(\ne\)\(\pm\)
\(\Leftrightarrow\) \(\dfrac{\left(x+1\right)^2}{\left(x+1\right) \left(x-1\right)}+\dfrac{3x\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}=\dfrac{4\left(x+1\right)\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}\)
\(\Leftrightarrow\) x2 + 2x + 1 + 3x2 - 3x = 4(x2 - 1)
\(\Leftrightarrow\) 4x2 - x + 1 = 4x2 - 4
\(\Leftrightarrow\) 4x2 - 4x2 - x = -1 - 4
\(\Leftrightarrow\) -x = -5
\(\Leftrightarrow\) x = 5 (tmđk)
Vậy................
Bài 2.
\(\left|x+2\right|< 2x+10\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}-2x-10< x+2\\x+2>2x+10\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}-2x-x< 10+2\\x-2x>10-2\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}-3x< 12\\-x>8\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}x>4\\x< 8\end{matrix}\right.\)
\(\Leftrightarrow\) 4 < x < 8
Vậy........................
