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Gringo123
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Can anyone explain to me what approach I need to take to solve this type of problem?
Express x/3x+1 - 2/8x-1
Express x/3x+1 - 2/8x-1
No. Show us what you got before you factored the numerator.Gringo123 said:Thanks Tim
The answer that I have come up with is:
(8x - 1) (x + 1) / 3x + 1) (8x - 1)
Is that correct?
If what you got previously was correct, then yes, this would be valid. However, instead of writing x + 1 / 3x - 1, you need parentheses around the numerator and denominator, like this (x + 1) / (3x - 1). Note that this isn't the right answer.Gringo123 said:If it is, can I not cancel out the (8x - 1) from the top and bottom, leaving me with just:
x + 1 / 3x - 1
?
Surely not, and you have made at least two errors coming up with this. Cancelling means removing factors that are the same in numerator and denominator.Gringo123 said:and then surely I can cancel x + 1 / 3x - 1 further to just x / 3x?
Use parentheses. The above should be written as x/(3x + 1) - 2/(8x - 1). If a numerator or denominator has more than one term, you need to surround it with parentheses.Gringo123 said:This is how I arrived at x + 1 / 3x + 1:
* x/3x + 1 - 2/ 8x-1
Use = to indicate that expressions are equal. Except for the first line, everywhere you have used * you should have =.Gringo123 said:* x(8x - 1) - 2(3x + 1) / (3x + 1) (8x - 1)
You skipped a step in the above, and one of your terms in the numerator is wrong.Gringo123 said:* 8x squared - x - 6x - 1 / (3x + 1) (8x - 1)
Aside from the fact that 8x2 - 7x - 1 is incorrect, the factorization is not (8x - 1)(x + 1). As problems get more involved, check your work in intermediate steps. Does (8x - 1)(x + 1) multiply to 8x2 - 7x - 1?Gringo123 said:* 8x squared - 7x - 1 / (3x + 1) (8x - 1)
* (8x - 1) (x + 1) / (3x + 1) (8x - 1)
Gringo123 said:* (x + 1) / (3x + 1)
The approach is the same as for adding two fractions, such as 3/8 + 1/6.Gringo123 said:Can anyone explain to me what approach I need to take to solve this type of problem?
Express x/3x+1 - 2/8x-1
To express a single fraction, you must combine or simplify the numerator and denominator into one fraction.
The process for expressing a single fraction involves finding a common denominator, adding or subtracting the fractions, and then simplifying the resulting fraction.
Yes, fractions with different denominators can be expressed as a single fraction by finding a common denominator and adding or subtracting the fractions.
Yes, it is important to simplify the resulting fraction when expressing as a single fraction to ensure the fraction is in its simplest form.
No, expressing as a single fraction involves combining or simplifying fractions, while converting to a decimal involves dividing the numerator by the denominator.