Question

R+1/S=1,
S+1/T=1
Then
RxSxT: ?​

Answer 1

$R\times S\times T=\frac{(S-1)(T-1)}{S}$

Step-by-step explanation:

Given : $R+\frac{1}{S}=1$ and $S+\frac{1}{T}=1$

To find : The value of $R\times S\times T$ ?

Solution :

Solve $R+\frac{1}{S}=1$

$\frac{RS+1}{S}=1$

$RS+1=S$

$RS=S-1$ ....(1)

Solve $S+\frac{1}{T}=1$

$\frac{ST+1}{T}=1$

$ST+1=T$

$ST=T-1$ ....(2)

Multiply (1) and (2),

$RS\times ST=(S-1)\times (T-1)$

$R\times S\times T=\frac{(S-1)(T-1)}{S}$

Therefore, $R\times S\times T=\frac{(S-1)(T-1)}{S}$

#Learn more

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Answer 2

$Given \: R + \frac{1}{S} = 1 \: ---(1)$

$and \: S + \frac{1}{T} = 1 \: ---(2)$

/* From (1) and (2) , we get */

$R + \frac{1}{S} = S + \frac{1}{T}$

$\implies \frac{SR + 1 }{S} = \frac{ST + 1}{T}$

$\implies T( SR + 1 ) = S( ST + 1)$

$\implies SRT + T = S^{2} T + S$

$\implies RST = S^{2} T + S - T$

Therefore.,

$\red {R\times S \times T} \green {=S^{2} T + S - T }$

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