Algebraic Fractions

Front

What is an algebraic fraction?

Back

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

Front

Simplify: 4(x+5)/3(x+5)

Back

4/3

Front

What is the first step in simplifying an algebraic fraction?

Back

Factor both the numerator and the denominator if possible.

Front

Simplify the algebraic fraction: 2pq/4p

Back

pq/2

Front

What does it mean to simplify an algebraic fraction?

Back

To reduce the fraction to its simplest form by canceling common factors.

Front

Simplify: (x^2 - 1)/(x - 1)

Back

x + 1 (after factoring the numerator as (x - 1)(x + 1) and canceling the common factor).

Front

What is a common factor in algebraic fractions?

Back

A common factor is a number or expression that divides both the numerator and the denominator without leaving a remainder.

Front

Simplify: 6x^2/9x

Back

2x/3 (by dividing both the numerator and denominator by 3x).

Front

What is the result of multiplying two algebraic fractions?

Back

Multiply the numerators together and the denominators together.

Front

Simplify: 2/(3/4)

Back

8/3 (by multiplying by the reciprocal of the fraction in the denominator).