simplify x-2/8x to the 2nd power - 32
You need to add parentheses in order to clarify the problem.
[(x-2)/8x]2 or just what?
You probably mean
(x-2)/(8x^2-32) = (1/8)*(x-2)/(x^2 -4)
Now factor the denominator and cancel the (x-2) in the numerator.
You should end up with 1/[8(x+2)]
5x+9>49
To simplify the expression x - (2/8x)^2 - 32, we can break it down into smaller steps.
Step 1: Simplify the term (2/8x)^2
To simplify this term, we need to square both the numerator (2/8) and the denominator (x).
Numerator:
(2/8)^2 = (1/4)^2 = 1/16
Denominator:
(x^2)
Now, we have (1/16)/(x^2).
Step 2: Rewrite the expression with the simplified term
Now, our expression becomes x - (1/16)/(x^2) - 32.
Step 3: Simplify the expression further
To simplify this expression, we need a common denominator for the terms. The common denominator will be x^2, so we need to rewrite the first term (x) in terms of x^2.
Multiply the numerator and denominator of the first term (x) by x:
(x/x) = x
Now, our expression becomes x^2/x^2 - (1/16)/(x^2) - 32.
Step 4: Combine like terms
The first term, x^2/x^2, simplifies to 1 because any number divided by itself is 1.
Now, our expression becomes 1 - (1/16)/(x^2) - 32.
Step 5: Simplify the expression further
To simplify the term (1/16)/(x^2), we need to multiply the numerator and denominator of the term by 16.
Numerator:
(1/16) * 16 = 1
Denominator:
(x^2) * 16 = 16x^2
Now, our expression becomes 1 - (1/16x^2) - 32.
Step 6: Combine the terms
Now, we have 1 - 1/16x^2 - 32.
Step 7: Simplify the expression further
To subtract (1/16x^2) from 1, we need a common denominator. The common denominator will be 16x^2, so we rewrite the first term, 1, in terms of 16x^2.
Multiply the numerator and denominator of the first term (1) by 16x^2:
(16x^2/16x^2) = 16x^2
Now, our expression becomes 16x^2 - 1/16x^2 - 32.
Step 8: Combine like terms
We cannot combine the terms 16x^2 and -1/16x^2 because they are not like terms.
Therefore, the simplified expression is 16x^2 - 1/16x^2 - 32.