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

Rational 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

There are no real numbers that satisfy the equation (make it true); there are no x-intercepts.

What are two interpretations of the statement "There are no real solutions."

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

Why can you not take the fourth root of a negative number?

can never be negative

400

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

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

500

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

What are: x = 0, x = 3/4, x = -1/2

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

400

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

What are: x = 5 - 2 root 7 (extraneous); x = 5 + 2 root 7

500

The solution(s) of: (7x + 13)^1/3 = x + 1

What are: x = -3, x = +/- 2

Rational Exponent Equations

100

The solution(s) of: 4x^(3/2) - x^(3/2) = 24

What is: x = 4

200

The solution(s) of: 5x^-2 - 3x^-1 - 1 = 0

What are: x = (-3 +/- root 29) / 2

300

Simplify: (2x³)⁴ / 16x⁵

x⁷

400

The solution(s) of: x^(4/3) - 13x^(2/3) + 36 = 0

What are: x = +/- 27, x = +/- 8

500

The solution(s) of: x^(7/6) - 16x^(1/2) + 3x^(2/3) - 48 = 0

What are: x = 9 (extraneous); x = 64