Question

verify the property: x× (y+z) = x×y + x×z by taking: x = -3/7, y= 12/13, z= -5/6​

Answer 1

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LHS = RHS

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Answer 2

$x \times (y + z) = xy + xz$

$x = \frac{ - 3}{7}$

$y = \frac{12}{13}$

$z = \frac{ - 5}{6}$

LHS

$\implies \: x \times (y + z) = \frac{ - 3}{7} \times ( \frac{12}{13} + \frac{ - 5}{6} )$

$= \frac{ - 3}{7} \times ( \frac{72 - 65}{78} )$

$= \frac{ - 3}{7} \times \frac{7}{78}$

$= \frac{ - 3}{78}$

$= \frac{ - 1}{26}$

RHS

$\implies \: xy + xz = ( \frac{ - 3 \times 12}{7 \times 13} ) + ( \frac{ - 3 \times - 5}{7 \times 6} )$

$= ( \frac{ - 36}{91} ) + ( \frac{15}{42} )$

$= \frac{ - 36}{91} + \frac{5}{14}$

$= \frac{ - 504 + 455}{1274}$

$= \frac{ - 49}{1274}$

$= \frac{ - 1}{26}$

LHS = RHS