Name Date _________ HSA.REI.B.4.B Class

Solve equations with rational expressionsKey Takeaways:

Standard: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

To solve equations that contain rational expressions we can:1. Simplify the expressions on both sides of the equation (if possible)2. Cross multiply and set the cross products equal to one another3. Solve the equation

Vocabulary: Cross multiply, cross products, rational expressions______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Everybody Writes!________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Part 1: Activation of Prior Knowledge

1

Consider the cross products of the equations below.

45=1215

1211

= 65.5

What do you notice? _____________________________________________________________________________________________________________________________________________________________________________________________________________________

2

Part 2: Explore!

1. For what value(s) of x is the equation below true?

x+74

=−2 x8

2. Solve algebraically for x:

x+26

= 3x−1

3

Part 3: Independent Practice (MILD)

1. For which values of x is the equation below satisfied?

x2= 5x−3

(1) −5 and 2(2) 5 and −2(3) 5 and 2(4) −5 and −2

2. Find all values of x that satisfy the equation:

x+1x+5

=3x

3. 4

(a)-4(b)−14(c) 1

4(d)4

4. What is the solution set of the equation shown here? x+2x−2=−3x

(a) x=−2 , x=3(b) x=−3 , x=−2(c) x=−1 , x=6(d) x=−6 , x=1

5.

(a)−2(b)−3(c) −10(d)−15

Part 4: Independent Practice (MEDIUM)Solve each of the equations below:

1.5

2x= 3x+1

2.x

−15= 1x−8

x−63

= 116+x

3.

Part 5: Independent Practice (SPICY)

1. Use the equation y=x2−4 to graph and determine the following information.

6

Vertex: _____________________________

Y-Intercept: _________________________

Axis of Symmetry: ___________________

Zeros: __________________________

8)

7

Mathletes

1.

8

“”I’m a mathlete

2.

3.

Name Date _________ HSA.REI.B.4.B Class

Solve equations with rational expressionsExit Ticket

Directions: Complete each problem by showing ALL work. Don’t forget to use MOLE!

1. For what value(s) of x is the equation below true?

3x5

=2x3

(a) x=09

(b)All real numbers(c) No solutions(d) x=0 and x=3

2. For what values ofx is the equation below true?

x+22

=3 x−2x

(a)2 only(b)-2 only(c) 2 and -2(d)4 only

3) For which values of x is the equation below satisfied?

2x= x−9

−4

(1) 8 and 1(2) −8 and −1(3) 4 and 2(4) −4 and −2

Name Date _________ HSA.REI.B.4.B Class

Solve equations with rational expressionsHomework

Directions: Solve each problem. Show all work using MOLE.

1) What values of x satisfy the equation x8=4x+4?

(1) 4 and −8(2) −4 and 8(3) −4 and −8

10

(4) 4 and 8

2) Solve the equation below for x algebraically:

4x= x+8

−3

3) What is the solution to the equation below?x+3x

= x+3−5

4) For which values of x is the equation below satisfied?

2 (−9+4 x )=6(4−x)

a) 21b) 3c) 3

7d) −21

5) Which of the following equations has an axis of symmetry where x=3?

1) x2+3 x−22) x2−6 x+13) 2 x2+6 x−44) x2+6 x−2

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6) What is the value of g (−2 )wheng ( x )=−2 x2+7?

a) 15b) 1c) -1d) 23

7) Which equation represents the following function?

X Y3 24 55 8

a. y = 3xb. y= 3x -3c. y= 3x -7d. y= 13x

8. What is the solution set to the following equation?

3 x2+5 x+1=0

Solution set: __________________________________________

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