Question

Tìm x:

1) (x-2)/(x-1) = (x+4)/(x-7)

2) (x+4)/20=5/(x+4)

Answer 1

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

<=>(x-2)(x-7)=(x-1)(x+4)

<=>x²-9x+14=x²+3x-4

<=>x²-9x-x²-3x=-4-14

<=>-12x=-18

<=>x=\(\frac{3}{2}\)

2,\(\frac{x+4}{20}=\frac{5}{x+4}\)

<=>(x+4)²=100

<=>x²+8x+16=100

<=>x²+8x-84=0

<=>x²+14x-6x-84=0

<=>x(x+14)-6(x+14)=0

<=>(x-6)(x+14)=0

<=>\(\orbr{\begin{cases}x-6=0\\x+14=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=6\\x=-14\end{cases}}}\)