Question

21Which expression is equivalent to şx-ay-?1141X1V41113X-1글금o ----- 4글금 -2 121+X-

Answer 1

As per given by the question,

There are given that a expression,

$\frac{2}{3}x-\frac{1}{2}y-\frac{4}{5}$

Now,

To find the expression is equivalent to given expression,

We will go through the all option.

Then,

For option first.

$\begin{gathered} \frac{1}{3}x-\frac{1}{4}y-\frac{4}{5}+\frac{1}{3}x+\frac{1}{4}y=x(\frac{1}{3}+\frac{1}{3})-y(\frac{1}{4}-\frac{1}{4})-\frac{4}{5} \\ =\frac{2}{3}x-\frac{4}{5} \end{gathered}$

The option first is does not match with given expression.

Now,

For option second,

$\begin{gathered} \frac{1}{3}x-\frac{1}{4}y-\frac{4}{5}+\frac{1}{3}x-\frac{1}{4}y=x(\frac{1}{3}+\frac{1}{3})-y(\frac{1}{4}+\frac{1}{4})-\frac{4}{5} \\ =\frac{2}{3}x-\frac{1}{2}y-\frac{4}{5} \end{gathered}$

The option second is matched with given expression.

Now,

For option third;

$\begin{gathered} \frac{1}{3}x-\frac{1}{4}y-\frac{1}{5}-\frac{1}{3}x-\frac{3}{5}-\frac{1}{4}y=x(\frac{1}{3}-\frac{1}{3})-y(\frac{1}{4}+\frac{1}{4})-(\frac{1}{5}+\frac{3}{5}) \\ =-\frac{1}{2}y-\frac{4}{5} \end{gathered}$

The option third also does not match with given expression.

Now,

For option fourth;

$\begin{gathered} \frac{1}{3}x-\frac{1}{4}y+\frac{2}{5}+\frac{1}{3}x-\frac{2}{5}-\frac{1}{4}y=x(\frac{1}{3}+\frac{1}{3})-y(\frac{1}{4}+\frac{1}{4})+(\frac{2}{5}-\frac{2}{5}) \\ \frac{2}{3}x-\frac{1}{2}y \end{gathered}$

The option fourth also does not match with given expression.

So,

Only the option second is matched with given expression.

Hence, the option B is correct.