3x+2/3x-2 - 6/2+3x = 9x2/9x2-4 (đkxđ :3/2 , -3/2)
<=>3x+2/(3x-2).(3x+2) - 6/(3x-2).(3x+2) = 9x2/(3x-2).(3x+2)
=>3x+2 - 6 = 9x2
<=>3x-9x2=6+2
<=>3x-9x2=8
<=>3(x-3x)=8
<=>x-3x=8/3
<=>2x=8/3
<=>x=8/3 / 2
<=>x=4/3(thoải mãn)
vậy phương trình có nghiệm x = 4/3
bây giờ phải đi học thêm rồi phần b làm cũng tương tự phần a mà cố gắng lên nha
a) dkxd: \(x\ne\frac{2}{3};x\ne-\frac{2}{3}\)
\(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x^2-4}\\ \Leftrightarrow\frac{\left(3x+2\right)\left(3x+2\right)-6\left(3x-2\right)}{\left(3x-2\right)\left(3x+2\right)}=\frac{9x^2}{\left(3x-2\right)\left(3x+2\right)}\\ \Leftrightarrow\left(3x+2\right)^2-18x+12=9x^2\\ \Leftrightarrow9x^2+12x+4-18x+12=9x^2\\ \Leftrightarrow9x^2-9x^2+12x-18x=-12-4\\ \Leftrightarrow-6x=-16\\ \Leftrightarrow x=-\frac{16}{-6}=\frac{8}{3}\left(tmdkxd\right)\)
Vay phuong trinh co tap nghiem la S={8/3}
b)de sai roi , minh sua lai cho
dkxd : \(x\ne\frac{1}{5};x\ne\frac{3}{5}\)
\(\frac{3}{5x-1}+\frac{2}{3-5x}=\frac{4}{\left(1-5x\right)\left(5x-3\right)}\\ \Leftrightarrow\frac{3\left(3-5x\right)+2\left(5x-1\right)}{\left(5x-1\right)\left(3-5x\right)}=\frac{4}{\left(5x-1\right)\left(3-5x\right)}\\ \Leftrightarrow9-15x+10x-2=4\\ \Leftrightarrow-15x+10x=-9+2+4\\ \Leftrightarrow-5x=-3\\ \Leftrightarrow x=\frac{-3}{-5}=\frac{3}{5}\left(loai\right)\)
Vaay phuong trinh vo nghiem S=\(\varnothing\)
