Question

$If \: \frac{1}{p} - \frac{1}{q} - \frac{1}{r} = \frac{1}{36} \: and \: pq \: + \: qr = pr \: then \: find \: the \: value \: of \: r.$
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Answer 1

                      ANSWER                        

Multiply both sides with pqr.

You get qr-pr-pq = $\frac{pqr}{36}$

Substitute pr as pq + qr,

We get  qr-pq-qr-pq = $\frac{pqr}{36}$

-2pq = $\frac{pqr}{36}$

Cancel pq.

We get  -2 = $\frac{r}{36}$

r = -72

Answer 2

                      ANSWER                        

Multiply both sides with pqr.

You get qr-pr-pq = \frac{pqr}{36}36pqr

Substitute pr as pq + qr,

We get  qr-pq-qr-pq = \frac{pqr}{36}36pqr

-2pq = \frac{pqr}{36}36pqr

Cancel pq.

We get  -2 = \frac{r}{36}36r

r = -72

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