Question

1, Cho \(\dfrac{5a+3b}{5c+3d}\) = \(\dfrac{7a-10b}{7c-10d}\). CMR \(\dfrac{a}{b}\) = \(\dfrac{c}{d}\)

Answer 1

\(\dfrac{5a+3b}{5c+3d}=\dfrac{7a-10b}{7c-10d}\)

\(\Leftrightarrow\left(5a+3b\right)\left(7c-10d\right)=\left(5c+3d\right)\left(7a-10b\right)\)

\(\Leftrightarrow35ac-50ad+21bc-30bd=35ac-50bc+21ad-30bd\)

\(\Leftrightarrow-50ad-21ad=-50bc-21bc\)

=>-71ad=-71bc

=>ad=bc

hay a/b=c/d