Worksheet: Solving Rational Equations

Comprehension worksheet generated from the video "Solving Rational Equations".

A1.A.1.1Use knowledge of solving equations with rational values to represent, use and apply mathematical models (e.g., angle measures, geometric formulas, dimensional analysis, Pythagorean theorem, science, statistics) and interpret the solutions in the original context.

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Worksheet: Solving Rational Equations

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Vocabulary

Rational equation — An equation involving fractions where the numerator and/or denominator contain variables.
Least Common Multiple (LCM) — The smallest positive integer that is a multiple of two or more given integers, used to clear fractions in an equation.
Cross-multiply — A method used to solve equations involving two fractions set equal to each other, by multiplying the numerator of one fraction by the denominator of the other.
Factor — To express a polynomial as a product of two or more polynomials.

Questions

Watch the video carefully and answer the following questions based on the content presented.

Based on the first example shown in the video (at 0:06,

\frac{5}{8} - \frac{3}{5} = \frac{x}{10}

), what was the first step the narrator took to solve the equation, and why was it effective?

In the second example (at 1:47,

x + \frac{8}{x} = 6

), the equation was transformed into a quadratic equation. What were the two solutions for x after factoring?

For the equation

\frac{9}{x} = \frac{x}{4}

(shown at 3:46), the narrator used a specific method to solve it. Describe this method and state the final answer(s).

In the final example (at 8:40),

\frac{x}{x+5} - \frac{5}{x-5} = \frac{14}{x^2-25}

, what was the least common multiple (LCM) used to clear the fractions?

$x^2$
$x+5$
$(x+5)(x-5)$
$x-5$

Reflect on the different strategies presented in the video for solving rational equations (e.g., finding the LCM, cross-multiplication, factoring quadratic equations). When might each strategy be most appropriate, and why is it important to be familiar with multiple approaches?

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Worksheet: Solving Rational Equations

Vocabulary

Questions

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