Subtract.
7/x^2-7x - x/7x-49
To subtract the given expressions, we first need to find a common denominator for the fractions. The common denominator for x^2-7x and 7x-49 is (x-7)(x+7).
Rewriting the expression with the common denominator, we have:
7/(x^2-7x)-x/(7x-49)
To make the denominators the same, we need to multiply the first fraction by (7x-49)/(7x-49), and the second fraction by (x^2-7x)/(x^2-7x):
(7/(x^2-7x))(7x-49)/(7x-49)-x/(x^2-7x)
Simplifying, we have:
(49x-343)/(x^2-7x)-x/(x^2-7x)
Now that the denominators are the same, we can subtract the numerators:
(49x-343-x)/(x^2-7x)
Combining like terms, we have:
(48x-343)/(x^2-7x)
Therefore, the simplified expression after subtracting is (48x-343)/(x^2-7x).
To subtract the given expressions, we should first find a common denominator for both terms. The denominators are x^2 - 7x and 7x - 49.
Step 1: Factor the denominators:
x^2 - 7x can be factored as x(x - 7), and
7x - 49 can be factored as 7(x - 7).
Step 2: Rewrite the expression with the common denominator:
7/x^2 - 7x = 7/x(x - 7), and
x/7x - 49 = x/7(x - 7).
Step 3: Find the common denominator by multiplying the two factors from step 1:
The common denominator is x(x - 7) × 7(x - 7) = 7x(x - 7)^2.
Step 4: Rewrite both terms with the common denominator:
7/x^2 - 7x = (7 * 7(x - 7))/7x(x - 7)^2 = 49(x - 7)/7x(x - 7)^2, and
x/7x - 49 = (x * x)/7x(x - 7)^2 = x^2/7x(x - 7)^2.
Step 5: Subtract the two terms:
49(x - 7)/7x(x - 7)^2 - x^2/7x(x - 7)^2
Step 6: Combine the terms over the common denominator:
(49(x - 7) - x^2)/(7x(x - 7)^2)
Step 7: Simplify the expression if possible:
(49x - 343 - x^2)/(7x(x - 7)^2)
To subtract the given expression, we need to find a common denominator for the two fractions and then combine them. Let's break it down step by step:
Step 1: Simplify the expressions in the numerator and denominator of both fractions separately.
In the first fraction, 7/x^2 - 7x, we can't simplify it further.
In the second fraction, -x/7x - 49, we can simplify it as follows:
- (x/7x) can be simplified to -1/7.
Thus, the second fraction becomes -1/7 - 49.
Step 2: Find a common denominator (CD) for the two fractions.
The CD can be found by multiplying the denominators together, as CD = (x^2)(7x - 49).
Step 3: Rewrite the fractions using the common denominator.
The first fraction, 7/x^2 - 7x, can be rewritten as (7(7x - 49))/(x^2)(7x - 49).
The second fraction, -1/7 - 49, can be rewritten as (-1 - 49(7x - 49))/CD.
Step 4: Combine the fractions.
Now that we have a common denominator, we can subtract these two fractions by placing them over the same CD and simplifying the numerator as follows:
(7(7x - 49))/(x^2)(7x - 49) - (-1 - 49(7x - 49))/CD
Simplifying the numerators:
(49x - 343))/(x^2)(7x - 49) - (-1 - 343x + 2401)/CD
Combining the numerators:
(49x - 343 + 1 + 343x - 2401)/CD
Simplifying the numerator:
(392x - 2400)/CD
So, the subtracted expression is (392x - 2400)/CD.