Question

$\large\red{\sf{Question}}$

Which of these is greater than p
$\large{\sf{if \: p = \frac{5}{7} }}$
$\large{\sf{A \rightarrow \frac{1}{p - 1} }}$
$\large{\sf{ B \rightarrow\frac{1 + p}{p} }}$
$\large{\sf{C \rightarrow \frac{p}{p - 1} }}$
$\large\underline{\sf{D \rightarrow \frac{p - 1}{p + 1} }}$
​

Answer 1

We know that multiplying equal numbers on fractions is valid. For a little trick, let's multiply for simple values. We get $\rm{7p=5}$.

$\rm{\dfrac{1}{p-1}}$

$\rm{=\dfrac{7}{7p-7}}$

$\rm{=\dfrac{7}{5-7}}$

$\rm{=-\dfrac{7}{2}}$

$\rm{\dfrac{p+1}{p}}$

$\rm{=\dfrac{7p+7}{7p}}$

$\rm{=\dfrac{5+7}{5}}$

$\rm{=\dfrac{12}{5}}$

$\rm{\dfrac{p}{p-1}}$

$\rm{=\dfrac{7p}{7p-7}}$

$\rm{=\dfrac{5}{5-7}}$

$\rm{=-\dfrac{5}{2}}$

$\rm{\dfrac{p-1}{p+1}}$

$\rm{=\dfrac{7p-7}{7p+7}}$

$\rm{=\dfrac{5-7}{5+7}}$

$\rm{=-\dfrac{2}{12}}$

$\rm{=-\dfrac{1}{6}}$

So now here are,

$\rm{A:\ -\dfrac{7}{2}}$

$\rm{B:\ \dfrac{12}{5}}$

$\rm{C:\ -\dfrac{5}{2}}$

$\rm{D:\ -\dfrac{1}{6}}$

Hence

$\rm{B}$ is greater than $\rm{p}$.