Cái bài đầu giải BPT bn ghi cái dj ak ,mik cx k hỉu nữa

V mik giải bài 2 nghen, sửa lại đề bài đầu rồi mik giải cho

\(3x-3=|2x+1|\)

Điều kiện: \(3x-3\ge0\Leftrightarrow3x\ge3\Leftrightarrow x\ge1\)

\(\Leftrightarrow\orbr{\begin{cases}2x+1=3x-3\\2x+1=-3x+3\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x-3x=-1-3\\2x+3x=-1+3\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}-x=-3\\5x=2\end{cases}\Leftrightarrow\orbr{\begin{cases}x=3\left(n\right)\\x=\frac{2}{5}\left(l\right)\end{cases}}}\)

Vậy S={3}

Cài đề câu b ,bn xem lại nhé!

\(\frac{2x-3}{35}+\frac{x\left(x-2\right)}{7}>\frac{x^2}{7}-\frac{2x-3}{5}\)

\(\Leftrightarrow\frac{2x-3}{35}+\frac{5x\left(x-2\right)}{35}-\frac{5x^2}{35}+\frac{7\left(2x-3\right)}{35}>0\)

\(\Leftrightarrow2x-3+5x\left(x-2\right)-5x^2+7\left(2x-3\right)>0\)

\(\Leftrightarrow2x-3+5x^2-10x-5x^2+14x-21>0\)

\(\Leftrightarrow6x-24>0\)

\(\Leftrightarrow x>4\)

VẬY TẬP NGHIỆM CỦA BẤT PHƯƠNG TRÌNH LÀ :  S = {  \(x\text{\x}>4\)}

\(\frac{6x+1}{18}+\frac{x+3}{12}\le\frac{5x+3}{6}+\frac{12-5x}{9}\)

\(\Leftrightarrow\frac{6\left(6x+1\right)}{108}+\frac{9\left(x+3\right)}{108}\le\frac{18\left(5x+3\right)}{108}+\frac{12\left(12-5x\right)}{108}\)

\(\Leftrightarrow36x+6+9x+27\le90x+54+144-60x\)

\(\Leftrightarrow36x+6+9x+27-90x-54-144+60x\le0\)

\(\Leftrightarrow15x-165\le0\)

\(\Leftrightarrow x\le11\)

VẬY TẬP NGHIỆM CỦA BẤT PHƯƠNG trình ..........

tk mk nka !!! chúc bạn học tốt !!!

b) \(\frac{x-3}{x-2}+\frac{x+2}{x-4}=-1\)

\(\Rightarrow\frac{\left(x-3\right)\left(x-4\right)}{\left(x-2\right)\left(x-4\right)}+\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x-4\right)}=-1\)

\(\Rightarrow\frac{\left(x-3\right)\left(x-4\right)+x^2-4}{\left(x-2\right)\left(x-4\right)}=-1\)

\(\Rightarrow\frac{x^2-7x+12+x^2-4}{\left(x-2\right)\left(x-4\right)}=-1\)

\(\Rightarrow\frac{2x^2-7x+8}{\left(x-2\right)\left(x-4\right)}=-1\)

\(\Rightarrow\frac{2x^2-7x+8}{\left(x-2\right)\left(x-4\right)}=-1\)

.................

a) \(\frac{2}{x-1}+\frac{2x+3}{x^2+x+1}=\frac{\left(2x-1\right)\left(2x+1\right)}{x^3-1}\)

\(\Rightarrow\frac{2\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{\left(2x+3\right)\left(x-1\right)}{\left(x+1\right)\left(x^2+x+1\right)}=\frac{\left(2x-1\right)\left(2x+1\right)}{x^3-1}\)

\(\Rightarrow\frac{2\left(x^2+x+1\right)+\left(2x+3\right)\left(x-1\right)}{x^3-1}=\frac{\left(2x-1\right)\left(2x+1\right)}{x^3-1}\)

\(\Rightarrow\left(x^3-1\right)\left[2\left(x^2+x+1\right)+\left(2x+3\right)\left(x-1\right)\right]=\left(x^3-1\right)\left(2x-1\right)\left(2x+1\right)\)

\(\Rightarrow2\left(x^2+x+1\right)+\left(2x+3\right)\left(x-1\right)=\left(2x-1\right)\left(2x+1\right)\)

\(\Rightarrow2\left(x^2+x+1\right)+\left(2x+3\right)\left(x-1\right)-\left(2x-1\right)\left(2x+1\right)=0\)

\(\Rightarrow2x^2+2x+2+2x^2-2x+3x-3-\left(4x^2-1\right)=0\)

\(\Rightarrow2x^2+2x+2+2x^2-2x+3x-3-4x^2+1=0\)

\(\Rightarrow3x=0\)

\(\Rightarrow luon-dung-voi-moi-x\)

nhầm phải là

3x=0

=>không có giá trị x thỏa mãn yêu cầu

\(a,ĐKXĐ:x\ne\pm\frac{1}{2}\)

Ta có: \(\frac{2}{2x+1}-\frac{3}{2x-1}=\frac{4}{4x^2-1}\)

\(\Leftrightarrow2\left(2x-1\right)-3\left(2x+1\right)=4\)

\(\Leftrightarrow4x-2-6x-3=4\)

\(\Leftrightarrow-2x=9\)

\(\Leftrightarrow x=-\frac{9}{2}\)(Tm ĐKXĐ)

Vậy pt có nghiệm duy nhất \(x=-\frac{9}{2}\)

\(b,ĐKXĐ:x\ne\pm1;-3\)

Ta có: \(\frac{2x}{x+1}+\frac{18}{x^2+2x-3}=\frac{2x-5}{x+3}\)

\(\Leftrightarrow\frac{2x}{x+1}+\frac{18}{\left(x-1\right)\left(x+3\right)}=\frac{2x-5}{x+3}\)

\(\Leftrightarrow2x\left(x-1\right)\left(x+3\right)+18\left(x+1\right)=\left(2x-5\right)\left(x-1\right)\left(x+1\right)\)

\(\Leftrightarrow2x\left(x^2+2x-3\right)+18x+18=\left(2x-5\right)\left(x^2-1\right)\)

\(\Leftrightarrow2x^3+4x^2-6x+18x+18=2x^3-2x-5x^2+5\)

\(\Leftrightarrow9x^2+14x+13=0\)

\(\Leftrightarrow\left(9x^2+14x+\frac{49}{9}\right)+\frac{68}{9}=0\)

\(\Leftrightarrow\left(3x+\frac{7}{3}\right)^2+\frac{68}{9}=0\)

Pt vô nghiệm 

\(c,ĐKXĐ:x\ne1\)

Ta có: \(\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\)

\(\Leftrightarrow x^2+x+1+2x^2-5=x-1\)

\(\Leftrightarrow3x^2=3\)

\(\Leftrightarrow x^2=1\)

\(\Leftrightarrow x=\pm1\)

Kết hợp vs ĐKXĐ được x = -1

Vậy pt có nghiệm duy nhất x = -1

làm lần lượt nha(bài nào k bt bỏ qua)

\(a,\frac{2}{2x+1}-\frac{3}{2x-1}=\frac{4}{4x^2-1}\)

\(\Rightarrow\frac{2\left(2x-1\right)-3\left(2x+1\right)}{4x^2-1}=\frac{4}{4x^2-1}\)

\(\Rightarrow-2x-5=4\)

\(\Rightarrow-2x=9\)

\(\Rightarrow x=\frac{9}{-2}\)

\(ĐKXĐ:x\ne-1\)

Từ phương trình suy ra \(\frac{x^2-x+1}{x^3+1}+\frac{2x^2+1}{x^3+1}+\frac{2x^2\left(x-1\right)\left(x+1\right)}{x^3+1}=2x\)

\(\Leftrightarrow\frac{2x^4+x^2-x+2}{x^3+1}=2x\)

\(\Leftrightarrow2x^4+x^2-x+2=2x^4+2x\)

\(\Leftrightarrow x^2-3x+2=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\x-2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=1\\x=2\end{cases}}\left(tmđk\right)\)

Vậy tập nghiệm của phương trình \(S=\left\{1;2\right\}\)

Đặt x² + 2x = a ta có

\(\frac{1}{a-3}\)+ \(\frac{18}{a+2}\)= \(\frac{18}{a+1}\)

<=> a² - 15a + 56 = 0

<=> a = (7;8)

Thế vô tìm được nghiệm 

\(\frac{2}{x-1}+\frac{2x+3}{x^2+x+1}=\frac{\left(2x-1\right)\left(2x+1\right)}{x^3-1}\)

Quy đồng mẫu chung :

\(\frac{2.\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{\left(2x+3\right)\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\frac{\left(4x^2-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)

Sau đó ta khử mẫu:

\(\Rightarrow\)\(2x^2+2x+2+2x^2+x-3=4x^2-1\)

\(\Rightarrow\)\(2x^2+2x+2x^2+x-4x^2=-1-2+3\)

\(\Rightarrow\)\(3x=0\)

\(\Rightarrow\)\(x=0\)

Vậy bạn tự kết luận 

ĐKXĐ:    \(x\ne1\)

           \(\frac{2}{x-1}+\frac{2x+3}{x^2+x+1}=\frac{\left(2x-1\right)\left(2x+1\right)}{x^3-1}\)

\(\Leftrightarrow\)\(\frac{2\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{\left(2x+3\right)\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\frac{4x^2-1}{x^3-1}\)

\(\Leftrightarrow\)\(\frac{2x^2+2x+2}{x^3-1}+\frac{2x^2+x-3}{x^3-1}=\frac{4x^2-1}{x^3-1}\)

\(\Rightarrow\)\(2x^2+2x+2+2x^2+x-3=4x^2-1\)

\(\Leftrightarrow\)\(4x^2+3x-1=4x^2-1\)

\(\Leftrightarrow\)\(3x=0\)

\(\Leftrightarrow\)\(x=0\)   (thỏa mãn)

Vậy....

\(\frac{2\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{2x+3\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\)\(\frac{4x^2-1}{\left(x-1\right)\left(x^2+x+1\right)}\)

\(\Leftrightarrow2x^2+2x+2+2x^2-2x+3x-3\)\(=4x^2-1\)

\(\Leftrightarrow2x^2+2x^2-4x^2+2x-2x+3x=-1-2+3\)

\(\Leftrightarrow3x=0\)

\(\Leftrightarrow x=0\left(nhận\right)\)

Vậy S= {0}

\(\Rightarrow\sqrt{x^2-\frac{1}{4}+\sqrt{\left(x+\frac{1}{2}\right)^2}}=\frac{2x^3}{2}+\frac{x^2}{2}+\frac{2x}{2}+\frac{1}{2}\)

\(\Rightarrow\sqrt{x^2+x+\frac{1}{2}-\frac{1}{4}}=\sqrt{x^2+x+\frac{1}{4}}=x^3+\frac{x^2}{2}+x+\frac{1}{2}\)

\(\Rightarrow\sqrt{\left(x+\frac{1}{2}\right)^2}=x+\frac{1}{2}=x^3+\frac{x^2}{2}+x+\frac{1}{2}\)

\(\Rightarrow x^3+\frac{x^2}{2}+x+\frac{1}{2}-x-\frac{1}{2}=x^3+\frac{x^2}{2}=0\Rightarrow\frac{2x^3+x^2}{2}=0\)

\(\Rightarrow2x^3+x^2=0\Rightarrow x^2\left(2x+1\right)=0\Rightarrow\hept{\begin{cases}x^2=0\Rightarrow x=0\\2x+1=0\Rightarrow2x=-1\Rightarrow x=-\frac{1}{2}\end{cases}}\)

vậy x=0 và x=-1/2

a) \(\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\left(x\ne1\right)\)

\(\Leftrightarrow\frac{1}{x-1}+\frac{2x^2-5}{\left(x-1\right)\left(x^2+x+1\right)}-\frac{4}{x^2+x+1}=0\)

\(\Leftrightarrow\frac{1\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{2x^2-5}{\left(x-1\right)\left(x^2+x+1\right)}-\frac{4\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=0\)

\(\Leftrightarrow\frac{x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{2x^2-5}{\left(x-1\right)\left(x^2+x+1\right)}-\frac{4x-4}{\left(x-1\right)\left(x^2+x+1\right)}=0\)

\(\Leftrightarrow\frac{x^2+x+1+2x^2-5-4x+4}{\left(x-1\right)\left(x^2+x+1\right)}=0\)

\(\Leftrightarrow\frac{3x^2-3x}{\left(x-1\right)\left(x^2+x+1\right)}=0\)

\(\Leftrightarrow\frac{3x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=0\)

\(\Leftrightarrow\frac{3x}{x^2+x+1}=0\)

=> 3x=0

<=> x=0 (tmđk)