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,

`(2)/(3)x-(1)/(2)y-(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} (1)/(3)x-(1)/(4)y-(4)/(5)+(1)/(3)x+(1)/(4)y=x((1)/(3)+(1)/(3))-y((1)/(4)-(1)/(4))-(4)/(5) \\ =(2)/(3)x-(4)/(5) \end{gathered}`

The option first is does not match with given expression.

Now,

For option second,

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

The option second is matched with given expression.

Now,

For option third;

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

The option third also does not match with given expression.

Now,

For option fourth;

`\begin{gathered} (1)/(3)x-(1)/(4)y+(2)/(5)+(1)/(3)x-(2)/(5)-(1)/(4)y=x((1)/(3)+(1)/(3))-y((1)/(4)+(1)/(4))+((2)/(5)-(2)/(5)) \\ (2)/(3)x-(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.