Simplify. show and explain your work.

Hey there!!

First of all , let us learn the basic formula -

a² - b² = ( a - b ) ( a + b )

First , let's solve for the numerator

( x / x - 2 ) + x

The LCM would be ( x - 2 )

So, this would become

x + x² - 2x / x - 2

x² - x / x - 2

Now let's solve for the denominator

1 / x² - 4

We can write 4 as 2²

1 / x² - 2²

As we have discussed the formula a² - b² and now is the right time to implement it .

a = x , b = 2

1 / ( x - 2 ) ( x + 2 )

The total equation :

( x² - x / x - 2  ) / ( 1 / ( x - 2 ) ( x + 2 )  

Remember :

When we have a / b

We can also write it as ( a × 1 / b )

Over here ,

a = ( x² - x / x - 2  ) b =  ( 1 / ( x - 2 ) ( x + 2 )

( x² - x / x - 2  )  /  ( 1 / ( x - 2 ) ( x + 2 )  

( x² - x / x - 2  )  × ( x - 2 ) ( x + 2 )  

The two x-2 would get cancelled

(x² - x )(  x + 2) is the final answer

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step-by-step explanation:

about 0.75 hours

step-by-step explanation: