If $\frac{a}{b} > 1$ $a/b >1$ , and $c$ $c$ is a positive integer, prove that $\frac{a}{b} > \frac{a + c}{b + c}$ $a/b>(a+c)/(b+c)$ ?

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If $\frac{a}{b} > 1$ $a/b >1$ , and $c$ $c$ is a positive integer, prove that $\frac{a}{b} > \frac{a + c}{b + c}$ $a/b>(a+c)/(b+c)$ ?

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Answer 1 · 2017-07-22T19:24:58

See below.

Explanation:

Assuming $a > 0, b > 0$ $a > 0, b > 0$ , if $\frac{a}{b} > 1 \Rightarrow a > b$ $a/b > 1 rArr a > b$ then

$a b + a c > a b + b c$ $ab + ac > ab + bc$ or

$a (b + c) > b (a + c) \Rightarrow \frac{a}{b} > \frac{a + c}{b + c}$ $a(b + c) > b(a+c) rArr a/b > (a+c)/(b+c)$

Answer 2 · 2017-07-22T19:29:41

The assertion fails if $a, b < 0$ $a, b < 0$

Explanation:

The assertion fails if $a, b < 0$ $a, b < 0$

Consider $a = - 3$ $a=-3$ , $b = - 2$ $b=-2$ and $c = 1$ $c=1$

Then:

$\frac{a}{b} = \frac{- 3}{- 2} = \frac{3}{2} > 1$ $a/b = (-3)/(-2) = 3/2 > 1$

$\frac{a + c}{b + c} = \frac{- 3 + 1}{- 2 + 1} = \frac{- 2}{- 1} = 2 > \frac{3}{2}$ $(a+c)/(b+c) = (-3+1)/(-2+1) = (-2)/(-1) = 2 > 3/2$

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If $\frac{a}{b} > 1$ $a/b >1$ , and $c$ $c$ is a positive integer, prove that $\frac{a}{b} > \frac{a + c}{b + c}$ $a/b>(a+c)/(b+c)$ ?

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Explanation:

Explanation:

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If a/b >1ab>1a/b >1, and ccc is a positive integer, prove that a/b>(a+c)/(b+c)ab>a+cb+ca/b>(a+c)/(b+c) ?

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Explanation:

Explanation:

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If $\frac{a}{b} > 1$ $a/b >1$ , and $c$ $c$ is a positive integer, prove that $\frac{a}{b} > \frac{a + c}{b + c}$ $a/b>(a+c)/(b+c)$ ?