Question

Tìm x, biết :

a) \(\frac{x-3}{x+5}=\frac{5}{7}\) b) \(\frac{x-1}{x+2}=\frac{x-2}{x+3}\)

Answer 1

a) \(\frac{x-3}{x+5}=\frac{5}{7}\)

\(\Rightarrow\left(x-3\right).7=\left(x+5\right).5\)

\(\Rightarrow7x-21=5x+25\)

\(\Rightarrow7x-5x=25+21\)

\(\Rightarrow2x=46\)

\(\Rightarrow x=46:2\)

\(\Rightarrow x=23\)

Vậy \(x=23.\)

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

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

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

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

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

\(\Rightarrow2x+1=0\)

\(\Rightarrow2x=0-1\)

\(\Rightarrow2x=-1\)

\(\Rightarrow x=\left(-1\right):2\)

\(\Rightarrow x=-\frac{1}{2}\)

Vậy \(x=-\frac{1}{2}.\)

Chúc bạn học tốt!

Answer 2

a,

\(\frac{x-3}{x+5}=\frac{5}{7}\\ \Rightarrow\left(x-3\right).7=\left(x+5\right).5\\ \Rightarrow7x-21=5x+25\\ \Rightarrow7x-5x=25+21\\ \Rightarrow2x=46\\ \Rightarrow x=23\)

vậy x = 23

b,

\(\frac{x-1}{x+2}=\frac{x-2}{x+3}=\frac{\left(x-1\right)-\left(x-2\right)}{\left(x+2\right)-\left(x+3\right)}=\frac{1}{-1}=-1\\ \Rightarrow\frac{x-1}{x+2}=-1\\ \Rightarrow\left(x-1\right).1=\left(x+2\right).\left(-1\right)\\ \Rightarrow x-1=-x-2\\ \Rightarrow x+x=-2+1\\ \Rightarrow2x=-1\\ \Rightarrow x=\frac{-1}{2}\)

vậy x = \(-\frac{1}{2}\)

Answer 3

\(\frac{x-3}{x+5}\) = \(\frac{5}{7}\)=> (x-3).7=(x+5).5

7x- 21 = 5x +25

7x-5x-21=25

2x-21=25

2x=25+21=46

x=46/2=23. Vậy x=23
b) \(\frac{x-1}{x+2}\) =\(\frac{x-2}{x+3}\) => (x-1).(x+3)=(x-2)(x+2)

x²+3x-x-3=x²+2x-2x-4

x²+2x-3=x²-4

x²+2x=x²-1

2x=-1 =>x =\(\frac{-1}{2}\) . Vậy x= \(\frac{-1}{2}\)

Tick nha tick nha <3