Solving Rational Equations

Example

Flashback (Lecture 3)

Example Problem

Cross Multiply

Distribute Out

Solve

Recap

• Add fractions to get a single denominator on each side

• Cross multiply to get rid of denominators• Combine like terms and solve for x

WARNING

• Whenever you multiply both sides by something with an x in it, you risk creating an extra incorrect answer.

Example 2

Recap

• Add fractions to get a single denominator on each side

• Cross multiply to get rid of denominators• Combine like terms and solve for x• Plug in and check for extra (wrong)

answers

Solve for x:

a) x = 2

b) x = 2/3

c) x = 1/2

d) x = 1

e) None of the above

Solve for x:

D) x=1

Solve for m:

a) m= k/2-1/p

b) m= (3pk)/(2p-k)

c) m= (3pk)/(k-2p)

d) m= (-3pk)/(p+k)

e) None of the choices are correct.

pmk

132

C

Solving Radical Equations

dude.

Simple Example

Simple Example

Slightly more complicated example

Slightly more complicated example

Another example

Simply as much as you can BEFORE YOU SQUARE

Recap

• Simplify to get the roots by themselves – (if you can)

• Square both sides• Solve for x

Sometimes you can’t simplify first

WARNING

• Whenever you square both sides, you’re multiplying both sides by something with an x in it.

• Whenever you multiply both sides by something with an x in it, you risk creating an extra incorrect answer.

Simple Example

Slightly more complicated example

Slightly more complicated example

Recap

• Simplify to get the roots by themselves – (if you can)

• Square both sides• Solve for x• Plug in and check for extra incorrect

answers

Find the solution(s):

a) x= 121/25

b) x= 25/121

c) x=25

d) x=121

e) No solutions

xx 35

A