\(\frac{2x+3}{2x+1}-\frac{2x+5}{2x+7}=1-\frac{6x^2+9x-9}{\left(2x+1\right)\left(2x+7\right)}\)

\(\Leftrightarrow1+\frac{2}{2x+1}-1-\frac{2}{2x+7}-1=-\frac{6x^2+9x-9}{\left(2x+1\right)\left(2x+7\right)}\)

\(\Leftrightarrow\frac{4x+14-4x-2+6x^2+9x-9}{\left(2x+1\right)\left(2x+7\right)}=1\)

\(\Leftrightarrow\frac{6x^2+9x+3}{\left(2x+1\right)\left(2x+7\right)}=1\)

\(\Leftrightarrow\frac{6x^2+6x+3x+3}{\left(2x+1\right)\left(2x+7\right)}=1\)

\(\Leftrightarrow\frac{6x\left(x+1\right)+3\left(x+1\right)}{\left(2x+1\right)\left(2x+7\right)}=1\)

\(\Leftrightarrow\frac{3\left(2x+1\right)\left(x+1\right)}{\left(2x+1\right)\left(2x+7\right)}=1\)

\(\Leftrightarrow3x+3=2x+7\)

\(\Leftrightarrow x=4\)

giup minh voi cac bạn

Bài 3:

a) \(\left(x-6\right).\left(2x-5\right).\left(3x+9\right)=0\)

\(\Leftrightarrow\left(x-6\right).\left(2x-5\right).3.\left(x+3\right)=0\)

Vì \(3\ne0.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-6=0\\2x-5=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\2x=5\\x=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=\frac{5}{2}\\x=-3\end{matrix}\right.\)

Vậy phương trình có tập hợp nghiệm là: \(S=\left\{6;\frac{5}{2};-3\right\}.\)

b) \(2x.\left(x-3\right)+5.\left(x-3\right)=0\)

\(\Leftrightarrow\left(x-3\right).\left(2x+5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\2x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\2x=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\frac{5}{2}\end{matrix}\right.\)

Vậy phương trình có tập hợp nghiệm là: \(S=\left\{3;-\frac{5}{2}\right\}.\)

c) \(\left(x^2-4\right)-\left(x-2\right).\left(3-2x\right)=0\)

\(\Leftrightarrow\left(x^2-2^2\right)-\left(x-2\right).\left(3-2x\right)=0\)

\(\Leftrightarrow\left(x-2\right).\left(x+2\right)-\left(x-2\right).\left(3-2x\right)=0\)

\(\Leftrightarrow\left(x-2\right).\left(x+2-3+2x\right)=0\)

\(\Leftrightarrow\left(x-2\right).\left(3x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\3x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\3x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\frac{1}{3}\end{matrix}\right.\)

Vậy phương trình có tập hợp nghiệm là: \(S=\left\{2;\frac{1}{3}\right\}.\)

Chúc bạn học tốt!

Bài 4 xem lại đề nhé bác

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 !!!

13(x+3)+(x+3)(x-3)=6(2x+7)

13x+39+x^2-9-12x-42=0

x^2+x-12=0

x=3 và x=-4

**** cho mk nha!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

a) <=> \(6x^2-5x+3-2x+3x\left(3-2x\right)=0\)

<=> \(6x^2-5x+3-2x+9x-6x^2=0\)

<=> \(2x+3=0\)

<=> \(x=\frac{-3}{2}\)

b) <=> \(10\left(x-4\right)-2\left(3+2x\right)=20x+4\left(1-x\right)\)

<=> \(10x-40-6-4x=20x+4-4x\)

<=> \(6x-46-16x-4=0\)

<=> \(-10x-50=0\)

<=> \(-10\left(x+5\right)=0\)

<=> \(x+5=0\)

<=> \(x=-5\)

c) <=> \(8x+3\left(3x-5\right)=18\left(2x-1\right)-14\)

<=> \(8x+9x-15=36x-18-14\)

<=> \(8x+9x-36x=+15-18-14\)

<=> \(-19x=-14\)

<=> \(x=\frac{14}{19}\)

d) <=>\(2\left(6x+5\right)-10x-3=8x+2\left(2x+1\right)\)

<=> \(12x+10-10x-3=8x+4x+2\)

<=> \(2x-7=12x+2\)

<=> \(2x-12x=7+2\)

<=> \(-10x=9\)

<=> \(x=\frac{-9}{10}\)

e) <=> \(x^2-16-6x+4=\left(x-4\right)^2\)

<=> \(x^2-6x-12-\left(x-4^2\right)=0\)

<=> \(x^2-6x-12-\left(x^2-8x+16\right)=0\)

<=> \(x^2-6x-12-x^2+8x-16=0\)

<=> \(2x-28=0\)

<=> \(2\left(x-14\right)=0\)

<=> x-14=0

<=> x=14

Luffy , cậu sai câu c nhé , kia là -17 ạ => x=17/19

a) ĐKXĐ: x khác +2

\(\frac{x-2}{2+x}-\frac{3}{x-2}-\frac{2\left(x-11\right)}{x^2-4}\)

<=> \(\frac{x-2}{2+x}-\frac{3}{x-2}=\frac{2\left(x-11\right)}{\left(x-2\right)\left(x+2\right)}\)

<=> (x - 2)^2 - 3(2 + x) = 2(x - 11)

<=> x^2 - 4x + 4 - 6 - 3x = 2x - 22

<=> x^2 - 7x - 2 = 2x - 22

<=> x^2 - 7x - 2 - 2x + 22 = 0

<=> x^2 - 9x + 20 = 0

<=> (x - 4)(x - 5) = 0

<=> x - 4 = 0 hoặc x - 5 = 0

<=> x = 4 hoặc x = 5

làm nốt đi 

\(ĐKXĐ:x\ne\pm5\)

 \(\frac{3}{4\left(x-5\right)}+\frac{15}{50-2x^2}=\frac{-7}{6\left(x+5\right)}\)

\(\Rightarrow\frac{3\left(x+5\right)}{4\left(x-5\right)\left(x+5\right)}+\frac{30}{4\left(25-x^2\right)}=\frac{-7\left(x-5\right)}{6\left(x+5\right)\left(x-5\right)}\)

\(\Rightarrow\frac{3x+15}{4\left(x-5\right)\left(x+5\right)}+\frac{-30}{4\left(x-5\right)\left(x+5\right)}=\frac{-7\left(x-5\right)}{6\left(x+5\right)\left(x-5\right)}\)

\(\Rightarrow\frac{3x+15-30}{4\left(x-5\right)\left(x+5\right)}=\frac{-7\left(x-5\right)}{6\left(x+5\right)\left(x-5\right)}\)

\(\Rightarrow\frac{3x-15}{4\left(x-5\right)\left(x+5\right)}=\frac{-7\left(x-5\right)}{6\left(x+5\right)\left(x-5\right)}\)

\(\Rightarrow\frac{3\left(x-5\right)}{4\left(x-5\right)\left(x+5\right)}=\frac{-7\left(x-5\right)}{6\left(x+5\right)\left(x-5\right)}\)

\(\Rightarrow\frac{3}{4\left(x+5\right)}=\frac{-7}{6\left(x+5\right)}\)

\(\Rightarrow18\left(x+5\right)=-28\left(x+5\right)\)

\(\Rightarrow18\left(x+5\right)+28\left(x+5\right)=0\)

\(\Rightarrow46\left(x+5\right)=0\Leftrightarrow x+5=0\Leftrightarrow x=-5\)(ktm)

Vậy pt vô nghiệm