Question

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

Answer 1

Answer:

$\frac{-3}7 (\frac{12}{13} + \frac{5}6) = (\frac{-3}7 * \frac{12}{13}) + (\frac{-3}7 * \frac{5}6)$

Step-by-step explanation:

According to question:

x = $\frac{-3}7$

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

z = $\frac{5}6$

Now, we need to prove x(y+z) = xy+xz            

- distributive property of addition over multiplication

Lets form an equation:

$\frac{-3}7 (\frac{12}{13} + \frac{5}6) = (\frac{-3}7 * \frac{12}{13}) + (\frac{-3}7 * \frac{5}6)$

And now lets solve!!

LHS (Left Hand Side):

$\frac{-3}7 (\frac{12}{13} + \frac{5}6)$ =  $\frac{-3}7 ( \frac{65 + 72}{78})$        -combined the fractions

                 =  $\frac{-3}7 (\frac{137}{78})$            -added them

                 =  $\frac{411}{546}$

RHS (Right Hand Side):

$(\frac{-3}7 * \frac{12}{13}) + (\frac{-3}7 * \frac{5}6)$ =   $\frac{15}{42} + \frac{36}{91}$         -multiplied the brackets

                               =   $\frac{195 + 216}{546}$         -combined the fractions

                               =   $\frac{411}{546}$

Thus, LHS = RHS, $\frac{411}{546}$ = $\frac{411}{546}$

______________________________________

Hope it helps

Please mark as brainliest :)