& AM5.2d To Solve Rational Equations

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Presentation transcript:

11-2-16 & 11-3-16 AM5.2d To Solve Rational Equations Got ID? Quiz on this lesson on Thursday, 11/3 Test on Functions: Friday, 11/4

http://patrickjmt.com and www.khanacademy.org/ Active Learning Assignment? Let’s look at: http://patrickjmt.com and www.khanacademy.org/

Find the domain restrictions. Lesson: To Clear the Fractions: Find the domain restrictions. (Set denominator ≠ 0) Cross multiply OR Multiply EVERY term by the LCD, which allows the denominators to divide out. *

Set denominator ≠ 0 Thus: x ≠ 0 Find domain restrictions, solve, and check: Domain Restrictions? Set denominator ≠ 0 Thus: x ≠ 0 Use Literacy Strategies to outline steps. (Cross multiply) (Set equal to zero) (x + 2)(x + 2) = 0 (Factor) Check x = -2 x + 2 = 0 ü x = -2

ü Find domain restrictions, solve, and check: Domain Restrictions? Set denominator ≠ 0 Thus: x ≠ 0 Now, check 42 = x LCD = 14x Multiply every term by LCD: 4x + 42 = 5x ü 42 = x

Active Learning Assignment: P. 35 #15, 16 (Don’t forget the Domain restrictions) Quiz on these lessons on Thursday, 11/3 Test on Functions: Friday, 11/4

Multiply every term by the LCD Find domain restrictions, solve, and check: Domain Restrictions? Set denominator ≠ 0 Thus: x - 2 ≠ 0 → x ≠ 2 and x + 2 ≠ 0 → x ≠ -2 LCD? (x + 2)(x – 2) Multiply every term by the LCD

(Factor out the common term) (Set factors equal to zero & solve) (Reduce, simplify) (FOIL or distribute) (Combine like terms) (Set equal to zero) (Factor out the common term) 2 = 0 or x = 0 or x + 2 = 0 (Set factors equal to zero & solve) x = 0 or x = -2 No, x ≠ -2, but we need to check x = 0. Are we finished?

Thus, the only solution is x = 0 We cannot use -2, because it will zero out the denominator. If we try to check it: But, we can check x = 0 in: 0 in the denominator is undefined, therefore -2 is not a solution. ü Thus, the only solution is x = 0

Active Learning Assignment: P. 35 #15, 16, 25-27 (& Domain restrictions) Please go to these websites and explore: http://patrickjmt.com & www.khanacademy.org/ WOW: Keep your promises. Quiz on these lessons on Thursday, 11/3 Test on Functions: Friday, 11/4