Ms. Terkper's Digital Classroom

Unit 6: Rational Expressions & Equations (Math 20-1)

Simplify; add/subtract; multiply/divide; solve rational equations & applied problems (with domain restrictions & extraneous checks).

Restrictions (N.P.V.) LCD Cancel Common Factors Cross-Multiplication Extraneous Solutions

What You Should Be Able To Do

State non-permissible values (values that make a denominator zero).
Simplify rational expressions by factoring and cancelling common factors.
Add/subtract rational expressions using the LCD; simplify the result.
Multiply/divide rational expressions; simplify and state restrictions.
Solve rational equations and check for extraneous solutions; model contextual problems.

I can find all non-permissible values. I can factor & cancel to simplify. I can build an LCD and combine terms. I can multiply/divide and simplify. I can solve equations & check solutions. Progress autosaves to this device.

Video Library

Simplifying Rational Expressions

Factor, restrict, cancel, and simplify.

youtube.com – “rational expressions simplify factoring cancel”

Adding & Subtracting (LCD)

Build a common denominator and combine.

youtube.com – “adding subtracting rational expressions LCD”

Multiply/Divide & Cancel

Cancel before multiplying to simplify.

youtube.com – “multiply divide rational expressions cancel”

Solve Rational Equations

Restrictions, solving, and extraneous roots.

youtube.com – “solve rational equations extraneous solutions”

Interactive Tools

Restrictions & Simplify

Enter numerator and denominator (degree ≤ 2). The tool factors where possible, finds N.P.V., and cancels common linear factors.

Numerator \(a_n x^2 + b_n x + c_n\)

Denominator \(a_d x^2 + b_d x + c_d\)

Original Denominator Roots (N.P.V.)	Value

Add/Subtract with LCD (Linear/Linear)

Two terms \((a_1x+b_1)/(c_1x+d_1)\) and \((a_2x+b_2)/(c_2x+d_2)\).

Term 1

Term 2

Operation

Multiply / Divide Rational Expressions (Linear/Linear)

Left \((a_1x+b_1)/(c_1x+d_1)\)

Right \((a_2x+b_2)/(c_2x+d_2)\)

Operation

Solve Rational Equation (Linear/Linear)

Solve \(\dfrac{a_1x+b_1}{c_1x+d_1} = \dfrac{a_2x+b_2}{c_2x+d_2}\) or \(\dfrac{a_1x+b_1}{c_1x+d_1}=k\). Automatically checks restrictions & extraneous.

\(a_1\)

\(b_1\)

\(c_1\)

\(d_1\)

\(a_2\)

\(b_2\)

\(c_2\)

\(d_2\)

Right side

\(k\)

Unit 6 Quizzes

Quiz 1: Simplify & LCD

Restrictions, cancel common factors, build LCD.

Quiz 2: Multiply/Divide & Equations

Simplify products/quotients, solve equations & applications.

Downloadable Review

Quick Practice Scratchpad

Try: \(\dfrac{x^2-1}{x^2-5x+6}\) simplify; \(\dfrac{3}{x-4}+\dfrac{2}{x+1}\); \(\dfrac{x+2}{x-3}\cdot\dfrac{x-3}{2x}\); solve \(\dfrac{2x-1}{x+3}=\dfrac{x+5}{x-2}\).