AlgB Rational Equations

Vocabulary

100

A rational expression has a ___ in the numerator or denominator

polynomial

200

A value that makes an expression undefined

excluded value

300

When the numerator and denominator have no common factors it is in ___

simplest form

400

To divide fractions, multiply by the ___

reciprocal or inverse

500

A solution that creates a false solution

extraneous solution

Simplifying

100

(-36x^3)/(42x^2)

(-6x)/7

200

(2r-4)/(r-2

2

300

(15a-3)/24

(5a-1)/8

400

(x+6)/(x^2+5x-6)

1/(x-1

500

(x^2-11x+18)/(x^2+2x-8)

(x-9)/(x+4)

Add and Subtract

100

(5n)/(30m) + (2m+4n)/(30m)

(2m+9n)/(30m)

200

(x+y)/(18xy) - (6x+y)/(18xy)

(-5)/(18y)

300

(a+2b)/(6a^3) - (5a+4b)/(6a^3)

(-2a-b)/(3a^3)

400

(5v)/(v-3) + 5/(v+6)

(5v^2+35v-15)/(v^2+3v-18)

500

(4x)/(x+3) - (4x)/(x+6)

(12x)/(x^2+9x+18)

Multiply and Divide

100

(6(r+2))/20 xx (4r)/(6(r+2))

r/5

200

(4n)/(n-6) //(4n)/(8n-48)

8

300

1/(v+10) xx (10v+30)/(v+3)

10/(v+10)

400

((p+6)(p-4))/(p-4) xx 1/((p-4)(p-2))

(p+6)/(p^2-6p+8)

500

(49x+21)/(6x) //(42x+18)/6

7/(6x)

Solving Equations

100

Identify any excluded values: 

x/(x+3) = 8/(x+6)

-3 and -6

200

x/(x+4) = 2/x

x=4 or x=-2

300

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

x=1/2

400

7/(x+3) = x/4

x=-7 or x=4

500

x/2 + 12/x = 5

x=6 or x=4