11/9 & 11/10 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 find the least common multiple (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 that appears in either polynomial.

Front

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

Back

The LCM is (x + 4)(x - 4)(x + 8).

Front

What is the difference of squares?

Back

The difference of squares is a special product that states a^2 - b^2 = (a - b)(a + b).

Front

How do you factor the expression x^2 - 16?

Back

x^2 - 16 can be factored as (x - 4)(x + 4) using the difference of squares.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

How do you solve a rational equation?

Back

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

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What is the process of simplifying a rational expression?

Back

To simplify a rational expression, factor the numerator and denominator, cancel out any common factors, and rewrite the expression.