Solving Rational Equations

Front

What is a rational equation?

Back

A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and/or denominator are polynomials.

Front

How do you solve a rational equation?

Back

To solve a rational equation, find a common denominator, eliminate the fractions by multiplying both sides by that denominator, and then solve the resulting equation.

Front

What is the least common multiple (LCM)?

Back

The least common multiple of two or more expressions is the smallest expression that is a multiple of each of the expressions.

Front

What is the LCM of x^2 - 16 and x^2 + 4x - 32?

Back

(x + 4)(x – 4)(x + 8)

Front

What is the LCM of 3x^2 - 27 and 5x^2 + 10x - 75?

Back

15(x + 3)(x - 3)(x + 5)

Front

What does it mean to simplify a rational expression?

Back

Simplifying a rational expression means reducing it to its simplest form by factoring and canceling common factors in the numerator and denominator.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents.

Front

What is the difference between a numerator and a denominator?

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In a fraction, the numerator is the top part that represents how many parts are taken, while the denominator is the bottom part that represents the total number of equal parts.

Front

What is a common denominator?

Back

A common denominator is a shared multiple of the denominators of two or more fractions, allowing them to be combined or compared.

Front

How do you find the LCM of two polynomials?

Back

To find the LCM of two polynomials, factor each polynomial into its prime factors and take the highest power of each factor.