If a- b- c are positive- then frac -a-b-b-c- isAlways smaller than frac -a-b-Greater than frac -a-b- only a - bAlways greater than frac -a-b-Greater than frac -a-b- only a - b

Question

Toppr Admin · Accepted Answer

A-cb-c-gt-ab-x21D2-ab-bc-gt-ab-ca-x21D2-bc-gt-ca-x21D2-b-gt-a-x21D2-a-lt-b

If a, b, c are positive, then $\frac{a + b}{b + c}$ is
Always smaller than $\frac{a}{b}$
Greater than $\frac{a}{b}$ only if a > b
Always greater than $\frac{a}{b}$
Greater than $\frac{a}{b}$ only if a < b

$\frac{a + c}{b + c} > \frac{a}{b}$
$\Rightarrow a b + b c > a b + c a$
$\Rightarrow b c > c a$
$\Rightarrow b > a$
$\Rightarrow a < b$

If a, b, c are positive, then a+bb+c isAlways smaller than abGreater than ab only if a > bAlways greater than abGreater than ab only if a < b

a+cb+c>ab⇒ab+bc>ab+ca⇒bc>ca⇒b>a⇒a<b

If a, b, c are positive, then $\frac{a + b}{b + c}$ is
Always smaller than $\frac{a}{b}$
Greater than $\frac{a}{b}$ only if a > b
Always greater than $\frac{a}{b}$
Greater than $\frac{a}{b}$ only if a < b

$\frac{a + c}{b + c} > \frac{a}{b}$
$\Rightarrow a b + b c > a b + c a$
$\Rightarrow b c > c a$
$\Rightarrow b > a$
$\Rightarrow a < b$