solve it!!!!

$x+\dfrac{1}{zy}=\dfrac{1}{5}$

$y+\dfrac{1}{xz}=\dfrac{-1}{15}$

$z+\dfrac{1}{xy}=\dfrac{1}{3}$

FIND THE VALUE OF-: z-y/z-x

#Algebra

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`2 \times 3`	$2 \times 3$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

Assuming that there is a typo in the first equation,

Subtracting the 2nd eqn from the 3rd eqn,

$z - y + \frac{1}{x}(\frac{1}{y} - \frac{1}{z}) = \frac{1}{3} - \frac{-1}{15}$

$(z - y)(1 + \frac{1}{xyz}) = \frac{6}{15}$ ----- 4

Subtracting the 1st eqn from the 3rd eqn,

$z - x + \frac{1}{y}(\frac{1}{x} - \frac{1}{z}) = \frac{1}{3} - \frac{1}{5}$

$(z - x)(1 + \frac{1}{xyz}) = \frac{2}{15}$ ----- 5

Dividing 4 from 5,

$\frac{z-y}{z-x} = 3$

Kartik Sharma - 6 years, 4 months ago

Is there a typo in eqn 1 ... should it be $x+\frac{1}{yz}= \frac{1}{5}$

Michael Fischer - 6 years, 4 months ago

3 is the answer

SAUPARNA PAUL - 6 years, 4 months ago

Farman Saifi - 6 years, 4 months ago

the answer is 3

Dheeraj Agarwal - 6 years, 4 months ago

3 :D

Handayani Basuki - 6 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$