Algebraic Fractions

Front

What is an algebraic fraction?

Back

An algebraic fraction is a fraction where the numerator and/or the denominator are algebraic expressions.

Front

How do you simplify an algebraic fraction?

Back

To simplify an algebraic fraction, factor both the numerator and the denominator and then cancel out any common factors.

Front

Simplify the algebraic fraction: (2pq)/(4p)

Back

pq/2

Front

What is the first step in simplifying the fraction (x^2 - 1)/(x + 1)?

Back

Factor the numerator to get (x - 1)(x + 1)/(x + 1) and then cancel the common factor.

Front

Simplify the algebraic fraction: (3x^2)/(6x)

Back

x/2

Front

What does it mean to have a negative exponent in an algebraic fraction?

Back

A negative exponent indicates that the base should be taken as the reciprocal: a^(-n) = 1/a^n.

Front

Simplify the algebraic fraction: (5a^3)/(10a^2)

Back

a/2

Front

What is the result of simplifying the fraction (2x)/(4x^2)?

Back

1/(2x)

Front

What is the importance of finding the least common denominator (LCD) in algebraic fractions?

Back

The LCD is used to combine or compare fractions with different denominators.

Front

Simplify the algebraic fraction: (x^2 - 4)/(x - 2)

Back

x + 2 (after factoring the numerator as (x - 2)(x + 2) and canceling the common factor).