\(\frac{12}{x^2-4}-\frac{x+1}{x-2}+\frac{x+7}{x+2}=0\)
ĐKXĐ : \(x\ne\pm2\)
\(\Leftrightarrow\frac{12}{\left(x-2\right)\left(x+2\right)}-\frac{x+1}{x-2}+\frac{x+7}{x+2}=0\)
\(\Leftrightarrow\frac{12}{\left(x-2\right)\left(x+2\right)}-\frac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{\left(x+7\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow\frac{12}{\left(x-2\right)\left(x+2\right)}-\frac{x^2+3x+2}{\left(x-2\right)\left(x+2\right)}+\frac{x^2+5x-14}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow12-\left(x^2+3x+2\right)+x^2+5x-14=0\)
\(\Leftrightarrow12-x^2-3x-2+x^2+5x-14=0\)
\(\Leftrightarrow2x-4=0\)
\(\Leftrightarrow2x=4\)
\(\Leftrightarrow x=2\)( không tmđk )
=> Phương trình vô nghiệm
\(\frac{12}{x^2-4}-\frac{x+1}{x-2}+\frac{x+7}{x+2}=0\left(đk:x\ne2;-2\right)\)
\(\Leftrightarrow\frac{12}{\left(x-2\right)\left(x+2\right)}-\frac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{\left(x+7\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow12-\left(x^2+3x+3\right)+\left(x^2+5x-14\right)=0\)
\(\Leftrightarrow12-x^2+x^2-3x+5x-3-14=0\)
\(\Leftrightarrow2x-17+12=0\Leftrightarrow2x-5=0\Leftrightarrow x=\frac{5}{2}\left(tmđk\right)\)
\(\frac{12}{x^2-4}-\frac{x+1}{x-2}+\frac{x+7}{x+2}=0\left(x\ne\pm2\right)\)
\(\Leftrightarrow\frac{12}{\left(x-2\right)\left(x+2\right)}-\frac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{\left(x+7\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}=0\)
\(\Leftrightarrow\frac{12}{\left(x-2\right)\left(x+2\right)}-\frac{x^2+3x+2}{\left(x-2\right)\left(x+2\right)}+\frac{x^2+5x-14}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow\frac{12-x^2-3x-2+x^2+5x+14}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow\frac{2x+26}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Rightarrow2x+26=0\)
\(\Leftrightarrow x=-13\left(tm\right)\)
vậy x=-13 là nghiệm của phương trình
\(\frac{12}{x^2-4}-\frac{x+1}{x-2}+\frac{x+7}{x+2}=0.\)
\(\Leftrightarrow\frac{12}{\left(x-2\right)\left(x+2\right)}-\frac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{\left(x+7\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=0.\)
\(\Leftrightarrow\frac{12}{\left(x-2\right)\left(x+2\right)}-\frac{x^2+3x+2}{\left(x-2\right)\left(x+2\right)}+\frac{x^2+5x-14}{\left(x-2\right)\left(x+2\right)}=0.\)
\(\Leftrightarrow\frac{12-x^2-3x-2+x^2+5x-14}{\left(x-2\right)\left(x+2\right)}=0.\)
\(\Leftrightarrow\frac{2x-4}{\left(x-2\right)\left(x+2\right)}=0.\)
\(\Rightarrow2x-4=0\Rightarrow x=2\) ĐKXĐ: x khác 2, -2 nên không thỏa mãn x nào => pt vô nghiệm
sửa dòng 3 :))
<=> 12-(x^2+3x+2)+(x^2+5x-14)=0
<=> 12-x^2+x^2-3x+5x-2-14=0
<=>2x-4=0<=>x=4/2(ktmđk)
\(\frac{12}{x^2-4}-\frac{x+1}{x-2}+\frac{x+7}{x+2}=0ĐK:x\ne\pm2\)
\(\Leftrightarrow\frac{12}{\left(x+2\right)\left(x-2\right)}-\frac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{\left(x+7\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}=0\)
Khử mẫu : \(12-\left(x^2+2x+x+2\right)+x^2-2x+7x-14=0\)
\(\Leftrightarrow12-x^2-2x-x-2+x^2-2x+7x-14=90\)
\(\Leftrightarrow-4+2x=0\Leftrightarrow x=2\)ko thỏa mãn điều kiện
PT vô nghiệm
