Question

tìm hiệu x-y biết: \(\frac{x+3}{y+5}=\frac{x+5}{y+7}\)

 

Answer 1

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

<=> (x+3)(y+7) = (y+5)(x+5)

<=> xy + 7x + 3y + 21 = xy + 5y + 5x + 25

<=> xy - xy + 7x - 5x + 3y - 5y = 25 - 21

<=> 2x - 2y = 4

<=> 2(x-y) = 4

<=> x-y = 4/2 = 2

Vậy x-y = 2.

Answer 2

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

=> x+3 = y+5

=> x -y = 5 -3 = 2

vậy x -y = 2

Answer 3

Từ \(\frac{x+3}{y+5}=\frac{x+5}{y+7}\)

=>(x+3).(y+7)=(y+5).(x+5)

=>x(y+7)+3(y+7)=y(x+5)+5(x+5)

=>xy+7x+3y+21=yx+5y+5x+25

=>7x+3y+21=5y+5x+25

=>5x+2x+3y+21=2y+3y+5x+21+4

=>2x=2y+4

=>2x-2y=4

=>2(x-y)=4=>x-y=2

VẬy x-y=2

Answer 4

\(\frac{x+3}{y+5}=\frac{x+5}{y+7}\Rightarrow xy+7x+3y+21=xy+5x+5y+25\)\(\Leftrightarrow2x-2y=4\Leftrightarrow x-y=2\)