How do you solve equations involving rational expressions?

When asked to solve an equation involving rational expressions, you can use either method, whichever one floats your canoe:

  1. Eliminate the denominators, or.
  2. Write the expression on each side of the equation as a fraction (where the fractions have the same denominator).

How do you solve rational inequalities step by step?

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.

How do you solve rational equations with the same denominator?

When solving rational equations, first multiply every term in the equation by the common denominator so the equation is “cleared” of fractions. Next, use an appropriate technique for solving for the variable. Remember that an equation means you have an equal sign.

How do you multiply rational expressions?

To multiply rational expressions:

  1. Completely factor all numerators and denominators.
  2. Reduce all common factors.
  3. Either multiply the denominators and numerators or leave the answer in factored form.

How do you simplify rational expressions?

  1. Step 1: Factor the numerator and the denominator.
  2. Step 2: List restricted values.
  3. Step 3: Cancel common factors.
  4. Step 4: Reduce to lowest terms and note any restricted values not implied by the expression.

How do you solve rational exponents?

Equations in which a variable expression is raised to a rational exponent can be solved by raising both sides of the equation to the reciprocal of the exponent. The reason the expression is raised to the reciprocal of its exponent is because the product of a number and its reciprocal is one.

How do you multiply and divide rational expressions step by step?

Q and S do not equal 0.

  1. Step 1: Factor both the numerator and the denominator.
  2. Step 2: Write as one fraction.
  3. Step 3: Simplify the rational expression.
  4. Step 4: Multiply any remaining factors in the numerator and/or denominator.
  5. Step 1: Factor both the numerator and the denominator.
  6. Step 2: Write as one fraction.

How do you multiply and divide rational expressions?

How To: Given two rational expressions, divide them.

  1. Rewrite as the first rational expression multiplied by the reciprocal of the second.
  2. Factor the numerators and denominators.
  3. Multiply the numerators.
  4. Multiply the denominators.
  5. Simplify.

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