Answer:
or ![=5x-1](https://tex.z-dn.net/?f=%3D5x-1)
Step-by-step explanation:
One is given the following equation:
![5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}](https://tex.z-dn.net/?f=5x-%5Cfrac%7B%5Csqrt%7B9x%5E2-6x%2B1%7D%7D%7B1-3x%7D)
The problem asks one to simplify the expression, the first step in solving this equation is to factor the equation. Rewrite the numerator and denominator of the fraction as the product of two expressions. Remember the factoring patterns:
![(a-b)^2=a^2-2ab+b^2](https://tex.z-dn.net/?f=%28a-b%29%5E2%3Da%5E2-2ab%2Bb%5E2)
![=5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}](https://tex.z-dn.net/?f=%3D5x-%5Cfrac%7B%5Csqrt%7B9x%5E2-6x%2B1%7D%7D%7B1-3x%7D)
![=5x-\frac{\sqrt{(3x-1)^2}}{-(3x-1)}](https://tex.z-dn.net/?f=%3D5x-%5Cfrac%7B%5Csqrt%7B%283x-1%29%5E2%7D%7D%7B-%283x-1%29%7D)
Now simplify the numerator. Remember, taking the square root of a squared value is the same as taking the absolute value of the expression,
![=5x-\frac{\sqrt{(3x-1)^2}}{1-3x}](https://tex.z-dn.net/?f=%3D5x-%5Cfrac%7B%5Csqrt%7B%283x-1%29%5E2%7D%7D%7B1-3x%7D)
![=5x-\frac{|3x-1|}{-(3x-1)}](https://tex.z-dn.net/?f=%3D5x-%5Cfrac%7B%7C3x-1%7C%7D%7B-%283x-1%29%7D)
Rewrite the expression without the absolute value sign in the numerator. Remember the general rule for removing the absolute value sign:
or ![(-a-b) = b-a](https://tex.z-dn.net/?f=%28-a-b%29%20%3D%20b-a)
![=5x-\frac{|3x-1|}{-(3x-1)}](https://tex.z-dn.net/?f=%3D5x-%5Cfrac%7B%7C3x-1%7C%7D%7B-%283x-1%29%7D)
or ![=5x-\frac{-(3x-1)}{-(3x-1)}](https://tex.z-dn.net/?f=%3D5x-%5Cfrac%7B-%283x-1%29%7D%7B-%283x-1%29%7D)
Simplify both expressions, reduce by canceling out common terms in both the numerator and the denominator,
or ![=5x-\frac{-(3x-1)}{-(3x-1)}](https://tex.z-dn.net/?f=%3D5x-%5Cfrac%7B-%283x-1%29%7D%7B-%283x-1%29%7D)
or ![=5x-(1)](https://tex.z-dn.net/?f=%3D5x-%281%29)
Simplify further by rewriting the expression without the parenthesis, remember to distribute the sign outside the parenthesis by the terms inside of the parenthesis; note that negative times negative equals positive.
or ![=5x-(1)](https://tex.z-dn.net/?f=%3D5x-%281%29)
or ![=5x-1](https://tex.z-dn.net/?f=%3D5x-1)
XD
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Textbooks... Workbooks.
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I was once homeschooled, ya know.
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Let me walk you through the problems.
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First of all...
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we know the area of the garden. In order to find how many cups of fertilizer we need, we need to find THE AREA. Then, it's just a matter-of-fact of just multiplying the area by 1/8.
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2. Information not needed? OF COURSE!! The money. Why we need money in this problem?! We find NUMBER OF CUPS, not MONEY NEEDED.
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3. I need to determine how much cups of fertilizer I need. The answer? Oh, find the area. IT's 9 1/3 multiplied by 12, by the way. Then multiply the area by 1/8. BOOM!!
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Need any more help, ask away!!
Thank you for posting your question here at brainly. The choices based on the above question are the below, it can be found elsewhere.
A. 1/7 <span>mpg
B.
7 mpg
C.
35 mpg
D.
175 mpg
The </span>unit rate for the distance traveled to the amount of gasoline used is 7 mpg. The answer is B.
Answer:
(9 - 3) × (8 ÷ 2) = 6 × 4 = 24
Step-by-step explanation:
One of the solution