What is (x^2 - 9)/(x^2 + 5x + 6) in lowest terms?
A fraction like this simplifies only after you factor the top and the bottom. Cancellation happens between factors, never between single terms.
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1 lesson for “Simplifying rational expressions”
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Why can't I add the x's to the plain numbers?
Lena simplified 5x + 3 + 2x + 4 and wrote 14x. She combined everything into x's, mixing apples with bananas.
Try this lessonIs it rise over run or run over rise?
Kai found the slope through (2, 3) and (6, 11) and wrote 1/2. He divided the run by the rise.
Try this lessonWhat is the opposite of adding 7?
Owen solved x + 7 = 12 by computing 12 + 7 = 19. He added again instead of undoing the addition.
Try this lessonWhat is x when x^2 - 2x - 4 = 0?
Not every quadratic factors over the integers. The quadratic formula works for all of them, and it only asks you for three careful numbers.
Try this lessonWhere did the negative sign go?
A negative sign belongs to the number next to it. Keeping that number together can prevent an almost-correct equation from turning into the wrong answer.
Try this lessonWhich move comes first?
Isla solved 3x + 4 = 19 by writing 3x = 23, giving x = 23/3. She never removed the +4 before dividing.
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