Solving a rational equation that requires factoring (Precalculus)
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- Опубликовано: 15 окт 2024
- How to solve a rational equation step by step! Algebra tutorial!
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4:30 I love the AC method better for this. AC = 105 B = 22 Two numbers add up to 22 also multiply to get 105. Those two numbers would be 7 and 15.
I was taught to explicitly state extraneous solutions back in algebra 1 at every step. That way, we never forget the discontinuity which can sometimes disappear.
couldnt you make the denominators the same like this?
x(x+2)/(2x+5)(x+2) - (x+5)(2x+5)/(x+2)(2x+5) = 1
You could, but things get messy, and you will need to remove the denominator later anyway.
Also, be careful with inline representations of fractions:
Is 1/2x equivalent to
1/(2x) = (1/2)(1/x)
as a human might believe, or is it
(1/2)x = x/2
as required by the order of operations?
As an example, x=4:
1/(2•4) = (1/2)(1/4) = 1/8
vs.
(1/2) • 4 = 4/2 = 2 .
Nobody seems to agree on which is correct, so it's better to put a denominator in parentheses/brackets when that denominator contains multiplication, even if context makes it obvious:
x(x+2)/((2x+5)(x+2)) - (x+5)(2x+5)/((x+2)(2x+5)) = 1
@@epsi thats p interesting. Thanks for taking time out of ur day to teach me smth new :)
@@epsi I did this. It was pretty tedious, and took a long time to expand, but i still got the right answer :D
@@beaverosa5831
Yes, i did the same.
Then i saw the video and was very unhappy with that approach lol
4:38 why cant you use the quadratic formula?
Another way to solve it is move the (x + 5)/(x + 2) to the right side, convert 1 to (x + 2)/(x + 2), add, then cross multiply:
x / (2x + 5) = (2x + 7) / (x + 2)
x^2 + 2x = 4x^2 + 24x + 35
3x^2 + 22x + 35 = 0
(3x + 7)(x + 5) = 0
Hello just want to ask if it's ok to interchange the final result, what I mean is if we let the right side of the equation be on the left side, is the sign, could it be affected? Or is it really ok to interchange without changing the sign. Tnx
coll