Question

If a, b, c are in continued proportion, the expression $\frac{a^2+ab+b^2}{b^2+bc+c^2}$ can be simplified to

• A. $\frac{a+c}{a+b}$
• B. $\frac{a}{c}$
• C. $\frac{c}{a}$
• D. $\frac{a-c}{b}$

Answer 1

The correct option is B $\frac{a}{c}$

If $a,b,c$ are in continued proportion, then $b^2=ac$
$=>\frac{a^2+ab+b^2}{b^2+bc+c^2}=\frac{a^2+ab+ac}{ac+bc+c^2}=\frac{a(a+b+c)}{c(a+b+c)}=\frac{a}{c}$