HS Math Solutions - Algebra: Rational Functions

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Algebra: Rational Functions

Contents (4 topics • 14 videos)

Simplifying Rational Expressions

Introduction Videos

Simplifying Rational Expressions

Simplifying Rational Expressions of the Form \( \frac{a-x}{x-a} \)

Multiplying and Dividing Rational Expressions

Video Practice Problems Playlist on YouTube

Multiply.
\[ \frac{x^2-3x-18}{4x+8} \cdot \frac{2x^2-8}{x^2-8x+12} \]

Multiply.
\[ \frac{2x^2-5x-3}{x^2-16} \cdot \frac{x^2-8x+16}{2x^2+7x+3} \]

Multiply.
\[ \frac{x^3-27}{12-3x} \cdot \frac{6x-24}{3x^3+9x^2+27x} \]

Divide.
\[ \frac{2x^2+8x-42}{x^2+6x-7} \div \frac{5x-15}{x-x^2} \]

Divide.
\[ \frac{x^4+8x}{x^2+4x+4} \div \frac{x^3-2x^2+4x}{x^2-4} \]

Divide.
\[ \frac{3x^2-7x+2}{x^2-x} \div \big( 3x^3-x^2-12x+4 \big) \]

Find the missing expressions.
\[ \frac{x^2-2x-24}{x^2+7x+12} \cdot \frac{ \text{ ? }}{ \text{ ? }} = \frac{x+2}{x^2+2x-3} \]

Adding and Subtracting Rational Expressions

Video Practice Problems

Find the missing expression.
\[ \frac{ \text{ ? }}{2x^3-x^2-8x+4} - \frac{3x-2}{x^2-4} = \frac{3}{x-2} \]

Partial Fraction Decomposition

Introduction Videos Playlist on YouTube

Partial Fraction Decomposition - Distinct Linear Factors

Partial Fraction Decomposition - Repeated Linear Factors

Partial Fraction Decomposition - Quadratic Factors

Partial Fraction Decomposition - Improper Rational Expressions