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# Rational expressions

See attached file for full problem description.

Solve by factoring and using the principle of zero products. Remember to check.
2
30. - 9x + 14 = 0

2
34. x + 16x = 0

2
46. 3x - 7x = 20

2. The length of a rectangle garden is 4m greater than the width. The area of the garden is 2
96m Find the length and the width.

6. The height of a triangle is 3 cm less than the length of the base. The area of the triangle is 2
35cm . Find the height and the length of the base.

10. A women's volleyball league has 23 teams. What is the total number of games to be played if each team plays every other team twice?

20. The product of the page numbers on two facing pages of a book is 420. Find the page numbers.

Simplify
8 3
24. -76x y
____________
4 3
-24x y

2
46. m - 10m + 25
______________________
2
m - 25

Multiply and simplify.

5v + 5 v - 4v + 4
_______ . _____________
v-2 2
v - 1

2 2
34. x + x - 20 x + 10x + 25
____________ ÷ ___________________
2 2
x - 7x + 12 x - 6x + 9

Find the LCM.

2 2 2 2
30. a - 2ab + b , a - b , 3a + 3b

#### Solution Preview

Solve by factoring and using the principle of zero products. Remember to check.
2
30. - 9x + 14 = 0

Solution:

X^2 -9x +14 =0

(x-2)(x-7)= 0

(x-2) =0 (or) (x-7) =0

(x-2) =0 , (x-7)=0

x = 2 , x= 7

Plug in x=2 in the above equation, we get

(2)^2 -9(2) +14 =0
4-18+14=0

18-18 =0

0=0

It satisfies the equation.

Similarly, plug in x= 7 in the above equation, we get

(7)^2 -9(7) +14 =0
49-63+14=0
63-63=0
0=0

It satisfies the equation.

Hence, x= 2 and 7 are the roots of the above quadratic equation.

2
34. x + 16x = 0

Solution:

x^2 +16x= 0

x(x+16) =0
x=0 (or) x+16=0

x= -16

Therefore, the values of x = 0 and -16.

Plug in x=0 in the above equation.

(0)^2 +16(0) =0

0=0

It satisfies the equation.

Plug in x= -16 in the above equation.

(-16)^2 +16(-16) =0

256 - 256 =0

0=0

It satisfies the equation.

Hence, x = 0 and -16 are roots of the above quadratic equation.

2
46. 3x - 7x = 20

Solution:

3x^2 -7x -20 =0

3x^2 -12x+5x-20 =0

3x(x-4) +5(x-4)=0

(3x+5) (x-4)=0

(3x+5) =0 (or) (x-4) =0

3x =-5 , x=4

x= -5/3

Plug in x = -5/3 in the above equation, we get

3(25/9) +35/3 = 20

(25/3) +(35/3) =20

(60/3) ...

#### Solution Summary

This is a series of rational expression questions including least common multiple, operations on polynomials, word problems, and solving quadratic equations.

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