(q)/(3 q-9)-(3)/(4 q+12) =(7 q^2+6 q+63)/(24 q^2-216)

Name: Problem 339, Chapter 8: Elementary Algebra
Uploaded: 2021-07-23T18:37:43-08:00
Duration: 5 min 35 s
Channel: Sherrie Fenner
Description: (q)/(3 q-9)-(3)/(4 q+12) =(7 q^2+6 q+63)/(24 q^2-216)

step 1 All right, so we have Q over 3Q minus 9 minus 3 over 4 Q plus 12 equals 7 Q squared plus 6 Q plu

(q)/(3 q-9)-(3)/(4 q+12) =(7 q^2+6 q+63)/(24...

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Key Concepts

Rational Expressions

Rational expressions are fractions where the numerator and/or the denominator are polynomials. Understanding these expressions is essential for performing operations such as addition, subtraction, multiplication, and division on them, as well as for simplifying and solving equations where these expressions appear.

Common Denominators

When adding or subtracting rational expressions, it is necessary to rewrite each fraction with a common denominator. This process involves finding an expression that is a multiple of each original denominator so that the fractions can be combined into a single rational expression.

Factoring

Factoring is the process of breaking down a complex expression into products of simpler expressions or polynomials. In the context of rational expressions, factoring is a key step to simplify the expressions or to identify and cancel common factors from the numerator and the denominator.

Simplification of Rational Expressions

Simplifying rational expressions involves combining like terms, factoring numerators and denominators, and reducing the expression by canceling out common factors. This process is important to reduce the expression to its simplest form, which often makes further operations or solutions more transparent.

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