Question

1. Tìm x, biết rằng:

a) \(\frac{x+4}{x+3}\) = \(\frac{x+9}{x+4}\)

b) \(\frac{x-5}{x+3}\) =  \(\frac{x-4}{x+6}\)

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

2. Tìm hai số x và y, biết:

\(\begin{cases}5x+4y=110\\x:y=2:3\end{cases}\)

Answer 1

B1:

a) \(\frac{x+4}{x+3}=\frac{x+9}{x+4}\)

-->(x+4)(x+4)=(x+3)(x+9)

\(x^2\)+4x+4x+16=\(x^2\)+9x+3x+27

\(x^2-x^2\)+4x+4x-9x-3x= - 16+27

 - 4x=11

x=\(\frac{-4}{11}\)

b) \(\frac{x-5}{x+3}=\frac{x-4}{x+6}\)

-->(x-5)(x+6)=(x+3)(x-4)

\(x^2\)+6x-5x-30=\(x^2\)-4x+3x-12

\(x^2-x^2\)+6x-5x+4x-3x=30-12

2x=18

x=9

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

--> (3x-1)(2x+1)=3x.(2x-1)

\(6x^2\)+3x-2x-1=\(6x^2\)-3x

\(6x^2-6x^2\)+3x-2x+3x=1

4x=1

x=\(\frac{1}{4}\)

 

Answer 2