Algebraic Skills

Roots and Rational Expressions

100

Rewrite √25 as a rational exponent

25^1/2

200

Convert x^1/3 into radical form.

³√x

300

Evaluate 64^1/3

4

Simplifying Radicals

100

√20 + √45

Simplify

5√5

200

(√8 + √2) / √3

Simplify

√6

300

(√12 + √27) / (√3 + 1)

Simplify

(15 - 5√3) / 2

Factoring with Coefficients

100

Factor 3x + 6

3(x+2)

200

Factor x² - 9x + 20

(x-4)(x-5)

300

Factor 2x² + 7x + 3

(2x+1)(x+3)

Multiply/Divide Rational Expressions

100

Simplify (3/2n)÷(3/2n)

= 1

200

Simplify (-4n÷15) x (10÷-12n²)

^{(Don't forget Restrictions)}

= 2/9n

n ≠ 0

300

Simplify (6a²b²c÷3ab) ÷ 9ac²

^{(Don't forget restrictions!)}

=2b/9c

= c ≠ 0

Add/Subtract Rational Expressions

100

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

simplify

(-x + 7) / 2x

200

((x^2 + 4x + 3) / 3x) - ((2x + 2) / 2x)

Simplify

(x + 1) / 3

300

(3x^2 + 16x + 5)/(x^2-4x-21) - (x-5)/(x+3)

Simplify and list restrictions
(leave numerator expanded, denominator factored)

(2x^2 + 28x - 30)/(x-7)(x+3)

x ≠ -3, 7