Rational Equations

Excluded Values

100

What are the excluded values for the below equation?

1/(x-4)+2/(x+5)=4/(x-4)(x+5)

Excluded values:   x≠ -5, 4

200

What are the excluded values for the below equation?

1=(v+2)/(v-4)+(7v-42)/(v-4) 

v≠ 4

300

This are the excluded values for the following equation (28-7b)/(b-4) * 1/(b+10)=12

b≠ -10, 4

400

What are the excluded values for the following equation (x^2 - 16)/(x-9) * (x^2 + x -90)/(x^2 + 14x +40)

x≠ 9, -4, and -10

500

What are the excluded values for the below equation?

-2/(5x^2+5x)+7/(x+1)=4

x ≠ -1, 0

LCD

100

What is the LCD of the below equation?

1/(x-4)+2/(x+5)=4/(x-4)(x+5)

LCD: (x-4)(x+5)

200

What is the LCD of the below equation?

(r-4)/5r=1/5r + 1

LCD: 5r

300

What is the LCD of the below equation?

-2/(5x^2+5x)+7/(x+1)=4

LCD: 5x(x+1)

400

What is the LCD of the below equation?

1/v+(3v+12)/(v^2-5v)=(7v-56)/(v^2-5v)

LCD: v(v-5)

500

What is the LCD of the below equation?

1/(r-2)+1/(r^2-7r+10)=6/(r-2)

LCD: (r-2)(r-5)

Solve Equations

100

Find the solution(s) (if any) for the below equation:

1/n^2+1/n=1/2n^2

n= -1/2

200

Find the solution(s) (if any) for the below equation:

x-7/(x+7)=x/(x+7)

x= 1

(x=-7 is an extra. solution, so it's not a real solution)

300

Find the solution(s) (if any) for the below equation:

3x-(x+3)/(x-1)=2x

x= -1, 3

400

Find the solution(s) (if any) for the below equation:

(r+5)/(r^2-2r)-1=1/(r^2-2r)

r= -1, 4

500

Find the solution(s) (if any) for the below equation:

1/(r-2)+1/(r^22-7r+10)=6/(r-2)

r= 26/5

Solve Equations

100

Find the solution(s) (if any) for the below equation:

1/6x^2=1/2x+7/6x^2

x= -2

200

Find the solution(s) (if any) for the below equation:

1= (v+2)/(v-4)+(7v-42)/(v-4)

v=36/7

300

Find the solution(s) (if any) for the below equation:

1= 1/(x^2+2x)+(x-1)/x

x= -1

400

Find the solution(s) (if any) for the below equation:

1+(x^2-5x-24)/(3x)=(x-6)/(3x)

x= -3, 6

500

Find the solution(s) (if any) for the below equation:

1/(x-1)+5/(x-3)=x/(x-1)

x= 8

(x=1 is an extraneous solution, so it is not a real solution) 

Misc.

100

Find the roots of the below equation:

x^2-5x-24=0

x=8, -3

200

When do we have an extraneous solution?

When our solution is an excluded value. (i.e., when our solution is part of our domain restriction)

300

Find the roots of the below equation:

3x^2+5x-2=0

x=1/3, -2

400

Factor the below expression:

x^2-16

(x+4)(x-4)

500

Find the LCD and any excluded values for the equation below: 

5x/2+7x/10=4

LCD: 10

Excluded Values: None