Sort the following statements into Always True Sometimes Tru

Sort the following statements into Always True, Sometimes True, and Never True: The sum of a rational number and a rational number is a rational number. The sum of a rational number and an irrational number is an irrational number. The sum of an irrational number and an irrational number is an irrational number. The product of a rational number and a rational number is a rational number. The product of a rational number and an irrational number is an irrational number. The product of an irrational number and an irrational number is an irrational number. The product of an odd number and an odd number is an odd number. The absolute value of a number is positive. x - 3/x - 3 = 1 The graph of y = x^2 - 4/x - 2 is the same as the graph of y = x + 2

Solution

1 ) Always true

2 ) Always true

3 ) Always true

4 ) Always true

5 ) Always true

6 ) Someties true

7 ) Always true

8) Always true

9 ) Always true

10 ) Always true

Given that

y = (x² - 4 ) / (x - 2 ) = (x² - 2² ) / (x - 2 ) [ since, a² - b² = ( a + b ) ( a - b ) ]

y = ( x + 2 ) ( x - 2 ) / ( x - 2 )

y = x + 2

Hence,

The graph of   y = (x² - 4 ) / (x - 2 ) is same as y = x + 2