State the product in simplest form. Multiply the numerators, and then multiply the denominators. Simplify by finding common factors in the numerator and denominator. Simplify the common factors.

To reduce the fraction, cancel out expressions in the numerator and denominator that are exactly the same. Step 3: Rewrite any remaining expressions in the numerator and denominator. Step 1: Factor both the numerator and denominator of the fraction.

A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials. Here are some examples of rational expressions. The last one may look a little strange since it is more commonly written 4×2+6x−10 4 x 2 + 6 x − 10 .

To write a rational expression in lowest terms, we must first find all common factors (constants, variables, or polynomials) or the numerator and the denominator. Thus, we must factor the numerator and the denominator. Once the numerator and the denominator have been factored, cross out any common factors.

To find the restricted values of a rational expression:

1. Set the denominator equal to zero.
2. Solve the equation.
3. The solution or solutions are the restricted values.

It is important to state the restrictions before simplifying rational expressions because the simplified expression may be defined for restrictions of the original. In this case, the expressions are not equivalent.

Simplifying rational expressions will make the further calculations easier since the variables to work with will usually be smaller. To determine that a rational expression is in simplest form we need to make sure that the numerator and the denominator have no common variables.

Rational expressions and rational equations can be useful tools for representing real life situations and for finding answers to real problems. In particular, they are quite good for describing distance-speed-time questions, and modeling multi-person work problems.

To solve a rational inequality, we follow these steps:

1. Put the inequality in general form.
2. Set the numerator and denominator equal to zero and solve.
3. Plot the critical values on a number line, breaking the number line into intervals.
4. Take a test number from each interval and plug it into the original inequality.

Step 1: Write the inequality in the correct form. One side must be zero and the other side can have only one fraction, so simplify the fractions if there is more than one fraction. Step 2: Find the key or critical values.

A rational function will be zero at a particular value of x only if the numerator is zero at that x and the denominator isn’t zero at that x . In other words, to determine if a rational function is ever zero all that we need to do is set the numerator equal to zero and solve.

A rational function is defined as the quotient of polynomials in which the denominator has a degree of at least 1 . In other words, there must be a variable in the denominator. The general form of a rational function is p(x)q(x) , where p(x) and q(x) are polynomials and q(x)≠0 .

Step 1: Completely factor both the numerators and denominators of all fractions. Step 2: Change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. Step 3 : Cancel or reduce the fractions.

1 Answer. The first step in simplifying this expression is to evaluate the terms within the parenthesis – starting with the multiplication and following the rules for operations in math.