i didi thi question but i keep getting a wrong answer
( x^2+5) - (x^2-2)
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(x^2-4) (4-x^2)
THIS IS A RESTRICTIONS QUESTION PLEASE HELP
To simplify the expression, you can start by factoring the numerator and denominator to see if any terms cancel out.
Numerator:
(x^2 + 5) - (x^2 - 2)
Distribute the negative sign to the second term in the numerator:
x^2 + 5 - x^2 + 2
Combine like terms:
( x^2 - x^2 ) + ( 5 + 2 )
0 + 7
7
Denominator:
(x^2 - 4) - (4 - x^2)
Again, distribute the negative sign to the second term in the denominator:
x^2 - 4 - 4 + x^2
Combine like terms:
( x^2 + x^2 ) + ( -4 - 4 )
2x^2 - 8
Now, substitute the simplified numerator and denominator back into the original expression:
7 / (2x^2 - 8)
The restriction in this question is also provided as (x^2 - 4) and (4 - x^2) in the denominators. These expressions cannot be equal to zero, as division by zero is undefined. Solving them will give us the restrictions:
x^2 - 4 = 0
x^2 = 4
x = ±2
4 - x^2 = 0
-x^2 = -4
x^2 = 4
x = ±2
Therefore, the restrictions are x ≠ 2 and x ≠ -2.
You can use these restrictions to determine the domain of the original expression, making sure to exclude the values of x that are not allowable.