Solving Rational / Radical Equations

Rational Equations #1

100

The solution(s) of: 1 + 3/x = 4/x^2

What are: x = -4; x = 1

200

The solution(s) of: 4/x - 7/(x + 1) = 6/(x^2 + x)

What is: x = -2/3

300

A number that is obtained by solving an equation correctly, but is not actually a solution.

What is an extraneous solution?

400

The solution(s) of: 5/(x^2 - 1) - 2/(x + 1) = 6/(x - 1)

What is: x = 1/8

500

The solution(s) of: x/(x - 3) + 2/(x - 2) = (x - 4)/(x^2 - 5x + 6)

What are: x = 2 extraneous x = -1

Equations #2

100

The solution(s) of: 1 - 13/x + 36/x^2 = 0

What are: x = 4, x = 9

200

The solution(s) of: 5/(x - 2) + 3/x = 7/(x^2 - 2x)

What is: x = 13/8

300

The solution(s) of absolute value of x+4 = 2x-6

What is 10 and -2/3

400

The solution(s) of: 7/(x^2 - 4) - 3/(x + 2) = 5/(x - 2)

What is: x = 3/8

500

The solution(s) of: x/(x + 4) + 3/(x - 2) = (16 - 2x)/(x^2 + 2x - 8)

What are: x = -4 (extraneous); x = 1

Radical Equations #1

100

The solution(s) of: 2(x - 3)^1/2 + 1 = 7

What is: x = 12

200

The solution(s) of: (x + 5)^1/2 = x - 1

What are: x = -1 (extraneous), x = 4

300

What is the square root of -72

6i on the square root of 2

400

The solution(s) of: (x + 4)^1/2 - (x - 3)^1/2 = 2

What is: x = 57/16 extraneous --> no solution

Radical Equations #2

100

The solution(s) of: 0.5(x + 2)^1/2 - 4 = 1

What is: x = 98

200

The solution(s) of: (x + 3)^1/2 = x + 1

What are: x = -2 (extraneous), x = 1

300

What is the fifth root of -32?

-2

Other

100

The solution(s) of: x²+7x=-6

What are -6 and -1

200

The solution of: 2x-4x<-2

What is (1,infinity)

x>1

300

The solution(s) of (2x-1)²=25

What is -3 and -2

400

The discriminant tells me 

What is the nature (types) of roots/solutions

500

The solution(s) -6(1+2x)>6(2x-1)+2x

What is (neg infinity,0) or x<0