6.2 Multiplying and dividing rational expressions

Ideas in this lesson

Multiply factored expressions

Multiply numerators and denominators, cancel common factors and retain all original denominator restrictions.

Divide using reciprocals

Multiply by the reciprocal of the divisor. The divisor must be defined and nonzero.

Exclude divisor zeros

For division, exclude zeros of original denominators and every input that makes the original divisor zero.

Simplify signs

Opposite binomials differ by a factor of negative one. Factor out that sign before simplifying.

Multiply or divide by a polynomial treated as a rational expression over one

multiply or divide by a polynomial treated as a rational expression over one.

Construct a quotient of contextual models, simplify and evaluate it with consistent units (per-ticket, per-person, efficiency or rate ratios)

construct a quotient of contextual models, simplify and evaluate it with consistent units (per-ticket, per-person, efficiency or rate ratios).

Construct rational products/quotients satisfying a target, and explain rational closure and the nonzero-divisor condition rather than only calculating

construct rational products/quotients satisfying a target, and explain rational closure and the nonzero-divisor condition rather than only calculating.