Question

Giúp mik vs 
1. \(\frac{x+1}{x+5}=\frac{x+3}{x+2}\)

2.\(\frac{x-4}{x-7}=\frac{x-2}{x-1}\)

Tìm x nha 

Answer 1

1. \(\frac{x+1}{x+5}=\frac{x+3}{x+2}\)

\(\Leftrightarrow\left(x+1\right)\left(x+2\right)=\left(x+3\right)\left(x+5\right)\)

\(\Leftrightarrow\left(x+1\right)x+\left(x+1\right).2=\left(x+3\right)x+\left(x+3\right).5\)

\(\Leftrightarrow x^2+x+2x+2=x^2+3x+5x+15\)

\(\Leftrightarrow x^2+3x+2=x^2+8x+15\)

\(\Leftrightarrow x^2+3x-x^2-8x=15-2\)

\(\Leftrightarrow-5x=13\)

\(\Leftrightarrow x=\frac{-13}{5}\)

Vậy ...

Answer 2

Cảm ơn bn nha 

Answer 3

dễ mà bạn tự làm đi động não lên

Answer 4

2. \(\frac{x-4}{x-7}=\frac{x-2}{x-1}\)

\(\Leftrightarrow\left(x-4\right)\left(x-1\right)=\left(x-7\right)\left(x-2\right)\)

\(\Leftrightarrow\left(x-4\right)x-\left(x-4\right)=\left(x-7\right)x-\left(x-7\right).2\)

\(\Leftrightarrow x^2-4x-x+4=x^2-7x-2x+14\)

\(\Leftrightarrow x^2-5x+4=x^2-9x+14\)

\(\Leftrightarrow x^2-5x-x^2+9x=14\)

\(\Leftrightarrow4x=14\)

\(\Leftrightarrow x=\frac{7}{2}\)

Vậy ...

Answer 5

Cảm ơn bạn Lê Tài Bảo Châu nha 

Answer 6

1.

\(\Rightarrow\left(x+1\right)(x+2)=\left(x+5\right)\left(x+3\right)\) 

     \(x^2+2x+x+2=x^2+3x+5x+15\) 

    \(x^2+3x+2-x^2-8x-15=0\) 

  \(-5x-13=0\) 

    \(x=\frac{-13}{5}\) 

Vậy.......

2.

\(\Rightarrow\left(x-4\right)\left(x-1\right)=\left(x-7\right)\left(x-2\right)\) 

     \(x^2-x-4x+4=x^2-2x-7x+14\) 

    \(x^2-5x+4-x^2+9x-14=0\) 

   \(4x-10=0\) 

   \(x=\frac{5}{2}\) 

Vậy......

Answer 7

\(1.\frac{x+1}{x+5}=\frac{x+3}{x+2}\)

\(\Rightarrow\frac{x+1}{x+5}-\frac{x+3}{x+2}=0\)

\(\Leftrightarrow\frac{\left(x+1\right)\left(x+2\right)-\left(x+3\right)\left(x+5\right)}{\left(x+5\right)\left(x+2\right)}=0\)

\(\Leftrightarrow\frac{x^2+3x+2-\left(x^2+8x+15\right)}{\left(x+5\right)\left(x+2\right)}=0\)

\(\Leftrightarrow\frac{x^2+3x+2-x^2-8x-15}{\left(x+5\right)\left(x+2\right)}=0\)

\(\Leftrightarrow\frac{-5x-13}{\left(x+5\right)\left(x+2\right)}=0\)

\(\left(x+5\right)\left(x+2\right)\ne0\)

\(\Rightarrow-5x-13=0\Rightarrow-5x=-13\Rightarrow x=\frac{13}{5}\)

\(2.\frac{x-4}{x-7}=\frac{x-2}{x-1}\)

\(\frac{x-4}{x-7}-\frac{x-2}{x-1}=0\)

\(\frac{\left(x-4\right)\left(x-1\right)-\left(x-2\right)\left(x-7\right)}{\left(x-7\right)\left(x-1\right)}=0\)

\(\frac{x^2-5x+4-x^2+9x-14}{\left(x-7\right)\left(x-1\right)}=0\)

\(\frac{4x-10}{\left(x-7\right)\left(x-1\right)}=0\)

\(4x-10=0\Rightarrow4x=10\Rightarrow x=\frac{10}{4}\)