Solving a rational equation that requires factoring (Precalculus)

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How to solve a rational equation step by step! Algebra tutorial!

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#math #algebra #mathbasics
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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.

Sgth
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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.

kamarinelson
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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

BlaixenU_
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4:38 why cant you use the quadratic formula?

yesyesyes
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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

gtaeverrr
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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

mikerain