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Elimination Method of Finding Solution of a Pair of Linear Equations

Using the sut...

Question

Using the sutra shunyam samyasachchaye, solve the equations.
$\frac{3 x + 2}{5 x + 7} + \frac{x + 1}{3 x - 1}$

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Solution

Sum of numerators of two sides $= 3 x + 2 + x + 1 = 4 x + 3$ ..............(i)
Sum of denominators of two sides $= 5 x + 7 + 3 x - 1 = 8 x + 6$ .............(ii)
Ratio of (i) and (ii) is $1 : 2$
$4 x + 3 = 0$
$\Rightarrow 4 x = - 3$
$\Rightarrow x = \frac{- 3}{4}$

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