which number cann be used in place of the variable in each rational expression
a^2-b^2/a-b
What you have written equals a + b, because the numerator equals (a+b)(a-b); so the a-b term cancels the denominator.
Your question is unclear. Both a and b can be any number.
To identify the number that can be used in place of the variable in the rational expression (a^2 - b^2) / (a - b), we need to consider the algebraic restrictions.
In this case, the denominator (a - b) should not result in division by zero, as division by zero is undefined. Therefore, we need to find a number that makes the denominator zero, since any other value would work.
To find this value, we set the denominator equal to zero and solve for the variable:
a - b = 0
Now, we can add b to both sides of the equation:
a = b
So, for the expression (a^2 - b^2) / (a - b), any number that satisfies the condition a = b can be used in place of the variable.