Fully simplify.
start fraction, start fraction, 5, divided by, x, squared, end fraction, minus, one fifth, divided by, start fraction, x, divided by, 5, end fraction, plus, 1, end fraction
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To fully simplify the expression, we need to simplify each fraction separately and then combine them.
1. Simplifying the first fraction:
5 divided by x squared simplifies to 5/x^2.
2. Simplifying the second fraction:
One fifth divided by x/5 can be rewritten as (1/5) * (5/x) = 1/x.
3. Combining the fractions:
(5/x^2) - (1/x) + 1
To combine these fractions, we need a common denominator. The common denominator is x^2, so we need to multiply the numerator and denominator of the second fraction by x. This gives us:
(5/x^2) - (x/ x^2) + 1
Now we can combine the fractions:
(5 - x + x^2) / x^2 + 1
This can be simplified further, but we cannot fully simplify it without additional information or context.
To fully simplify the given expression, let's break it down step by step:
1. Simplify the numerator of the first fraction:
Start with the expression 5 / x^2.
Since there are no like terms to combine, this cannot be simplified further.
2. Simplify the denominator of the first fraction:
Start with the expression x / 5.
Again, no like terms to combine, so this cannot be simplified further.
3. Simplify the second fraction:
The expression 1 / 5 can be simplified by multiplying both the numerator and denominator by the reciprocal of 5, which is 1/5 itself.
This gives us 1 / 5 = 1 * (1 / 5) = 1/5.
4. Now, we can rewrite the original expression with the simplified fractions:
(5 / x^2) - (1/5) + 1
5. Since there are no like terms in the numerator and denominator, we cannot combine them. However, we can rewrite 1 as a fraction with the same denominator of 5:
1 = 5/5.
6. Rewrite the expression with the common denominator of 5:
(5 / x^2) - (1/5) + (5/5)
7. Simplify the numerators:
(5 / x^2) - (1/5) + (5/5) = (5 - 1)/x^2 + (5/5) = 4/x^2 + 1.
So, the fully simplified expression is 4 / x^2 + 1.
To simplify this expression, let's work step-by-step.
Step 1: Simplify within the second fraction in the numerator.
From the expression:
1/x ÷ 5 = 1/x × 1/5
Step 2: Simplify within the denominator.
The denominator is already simplified.
Step 3: Simplify the whole expression.
Now, we can rewrite the expression as follows:
(((5 ÷ x^2) - (1/5)) ÷ (x ÷ 5)) + 1
Step 4: Simplify the remaining fraction in the numerator.
The expression becomes:
(5/x^2 - 1/5) ÷ (x/5) + 1
Step 5: Simplify the complex fraction.
To simplify the complex fraction, we can multiply the numerator and denominator by the reciprocal of the denominator.
((5/x^2 - 1/5) ÷ (x/5) + 1) * (5/x)
Simplifying further is not possible without additional context or assumptions about the value of x.