plz help
a, b, c, and d are real numbers and a > c, b> d, a/b = c/d = r
Prove that a-c / b-d = r
Please use parenthesis. What you wrote is
$\displaystyle a - \frac{c}{b} - d$
To write it as you intended write (a - c)/(b - d) = r.
$\displaystyle \frac{a}{b} = r$ means that $\displaystyle a = br$
$\displaystyle \frac{c}{d} = r$ means that $\displaystyle c = dr$
So
$\displaystyle \frac{a - c}{b - d} = \frac{br - dr}{b - d} = \frac{r(b - d)}{b - d} = r$
-Dan
Hello, jenjen!
What have you tried?
. . It's fairly straight-forward.
From $\displaystyle \frac{a}{b} \:=\:r$, we have: .$\displaystyle a \:=\:br$ .[1]$\displaystyle a,\,b,\,c,\,d$ are real numbers, and: .$\displaystyle a > c,\;\;b> d,\;\;\frac{a}{b}\,=\,\frac{c}{d}\,= \,r$
Prove that: .$\displaystyle \frac{a-c}{b-d}\:=\:r$
From $\displaystyle \frac{c}{d} \:=\:r$, we have: .$\displaystyle c \:=\:dr$ .[2]
Subtract [2] from [1]: .$\displaystyle a - c \:=\:br - dr\quad\Rightarrow\quad a-c\:=\:(b-d)r$
Therefore: .$\displaystyle \frac{a - c}{b-d} \:=\:r$