Question

If $\frac{5x+6y}{5u+6y}=\frac{5x-6y}{5u-6y}$:
then prove that x: y = u: v

Answer 1

$\left(\frac{5x+6y}{5u+6v}\right)=\left(\frac{5x-6y}{5u-6v}\right)\left(\frac{5x+6y}{5x-6y}\right)=\left(\frac{5u+6v}{5u-6v}\right)usecomponendoanddividendo\left(\frac{5x+6y+5x-6y}{5x+6y-5x+6y}\right)=\left(\frac{5u+6v+5u-6v}{5u+6v-5u+6v}\right)(\frac{10x}{12y}=\frac{10u}{12v})or\frac{x}{y}=\frac{u}{v}proved$