
8 6 Skills Practice Solving Rational Equations and Inequalities Form


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People also ask 7 6 skills practice solving rational equations and inequalities
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How to identify a rational equation?
A rational equation is an equation that contains fractions with xs in the numerator, denominator or both. Here is an example of a rational equation: (4 / (x + 1)) - (3 / (x - 1)) = -2 / (x^2 - 1). Let's think back for a moment about solving an equation with a fraction. 1/3 x = 8.
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Why all solutions of a rational equation must be checked?
But because the original equation may have a variable in a denominator, we must be careful that we don't end up with a solution that would make a denominator equal to zero. So before we begin solving a rational equation, we examine it first to find the values that would make any denominators zero.
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Why should you check every solution of a radical equation?
When you square a radical equation you sometimes get a solution to the squared equation that is not a solution to the original equation. Such an equation is called an extraneous solution. Remember to always check your solutions in the original equation to discard the extraneous solutions.
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What have you learned about solving rational equations and inequalities?
To solve an equation involving rational functions, we cross multiply the numerators and denominators. Then we move all our terms to one side. Then we use our algebra skills to solve. To solve an inequality involving rational functions, we set our numerator and denominator to 0 and solve them separately.
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What are the steps in solving rational equations and inequalities?
How do you solve rational inequalities step by step? Step 1: Put the inequality in general form. ... Step 2: Find the zeros (solutions) of the numerator and the denominator. ... Step 3: Use the critical points from step 2 to divide the number line into intervals. Step 4: Choose a value in each interval.
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How do you solve rational equations 6th grade?
Strategy to Solve Equations with Rational Expressions Note any value of the variable that would make any denominator zero. Find the least common denominator of all denominators in the equation. Clear the fractions by multiplying both sides of the equation by the LCD. Solve the resulting equation. Check.
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Why is it important to check solutions to rational equations?
It is necessary to perform a check because in the process of multiplying through you can introduce spurious solutions.
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Why should you check solutions of rational equations and inequalities?
It's essential to verify solutions to ensure they are not extraneous, meaning they don't fit within the domain of the given problem. This lesson focuses on solving equations that contain one or more rational expressions.
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