Q:

# What are the ways of reducing rational expressions to lowest terms?

A:

Rational expressions are reduced to their simplest forms by factoring. Factoring allows the removal of the greatest common factors, which makes the expression have lower terms and not look as intimidating. Several factoring methods exist. Factoring by grouping and by removing the greatest common factors are the two most prominent.

## Keep Learning

Factoring by grouping involves rearranging the expressions by degree, grouping them into smaller parenthetical expressions and simplifying them. After removing common terms, the common terms are placed in their own group. For example, the expression x^4 + 3x^3 - x^2 + 5x simplifies to x^3(x + 3) - x(x + 5). In turn, this goes to (x^3 - x)(x + 3)(x + 5).

Factoring with the distributive property works similarly. For example, the expression (6x^2 -12x + 9)/(3x - 6) reduces to 3(x - 1)(x - 3)/3(x - 2). The 3 cancels out, leaving (x - 1)(x - 3)/(x - 2). This expression can be placed on a graph, leaving all real solutions except for 2, because 2 would make the denominator zero.

Radicals, such as square or cube roots, cannot occupy the denominator. If one occurs, the whole expression has to be squared or cubed to cancel out the radical and leave the expression in its simplest form.

Sources:

## Related Questions

• A: To solve multi-step equations in algebra, you need to collect like terms, simplify the expressions and follow the order of operations to isolate the variab... Full Answer >
Filed Under:
• A: Simplify rational expressions by factoring each polynomial to its simplest terms, then cancelling out like terms in the numerator and denominator. It may b... Full Answer >
Filed Under:
• A: The Purplemath solver is a website that offers lessons on ways to solve many forms of algebraic problems. It provides detailed steps on how to solve quadra... Full Answer >
Filed Under:
• A: X3y3 + z3 can be factored by using a graphing calculator or through factoring as a sum of cubes. The final answer for factoring x3y3 + z3 is (xy + z) times... Full Answer >
Filed Under:
PEOPLE SEARCH FOR