Unit 4 – Day 1 Name: Date: Integrated Math 4G: NOTES

Solving Rational Equations – LCM Method In Unit 2, we worked with rational expressions. In Unit 4, we will still be working with rational expressions, but they will be in the form of equations. We use the LCM method when we have _________________________________________________. Solve the following rational equations for 𝑥:

Ex 1) 7𝑥+ 3

4= 2

3𝑥 How to solve rational equations:

1) Find the LCM of the denominators in the problem by finding the prime factors of the denominators and multiplying them together.

2) Multiply EACH TERM by the entire LCM. If you find yourself needing to distribute, STOP! It makes it easier if you don’t!

3) Cancel what you can after multiplying.

4) You should be left with a regular equation, which you solve for 𝑥. All of your fractions should cancel!

Ex 2) 5𝑥+1

+ 𝑥𝑥2−1

= 7𝑥+1

more than two fractions (parts)

Unit 4 – Day 1

Ex 3) 32𝑥− 𝑥

3= 1

12

Always check for “extraneous solutions” – meaning solutions that give you 0 in the denominator of any fraction in your original problem. You try:

Ex 4) 1𝑥2+ 1

𝑥= 1

2𝑥2

Unit 4 – Day 1 Name: Date: Integrated Math 4G: CLWK

Solving Rational Equations – LCM Method

(#1-6) Solve each rational equation for 𝑥.

1) 32𝑥+ 7

5𝑥= − 29

30

2) 1𝑥− 𝑥

4= − 4

3

3) 5𝑥2−4

+ 5𝑥−2

= 6

Unit 4 – Day 1

4) 5𝑥− 6

𝑥2= 1

5) 2𝑥+ 𝑥

3= 11

6

6) 3𝑥+2

− 1𝑥= 1

5𝑥