Solving Quadratic Equations Involving Fractions (Leaving Cert Mathematics): Quizzes

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Solving Quadratic Equations Involving Fractions
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What are quadratic equations involving fractions also called?

Rational equations

What is the key technique for solving quadratic equations with fractions?

Multiply by the LCM of denominators

What is the first step when solving quadratic equations involving fractions?

Identify all denominators

Why is the LCM method the most efficient approach?

Removes all fractions in one step

For x−33+12x=4\frac{x-3}{3} + \frac{12}{x} = 4, what is the LCM of the denominators?

3x3x

What are the solutions to x−33+12x=4\frac{x-3}{3} + \frac{12}{x} = 4 after solving?

x=3x = 3 or x=12x = 12

For 2x−1−1x+2=12\frac{2}{x-1} - \frac{1}{x+2} = \frac{1}{2}, what is the LCM of denominators?

2(x−1)(x+2)2(x-1)(x+2)

What are the solutions to 2x−1−1x+2=12\frac{2}{x-1} - \frac{1}{x+2} = \frac{1}{2}?

x=4x = 4 or x=−3x = -3

What must you check about solutions in these equations?

They don't make denominators zero

What common mistake occurs when using the LCM method?

Forgetting to multiply ALL terms

After multiplying by the LCM, what type of equation results?

A standard quadratic equation

What should you do after finding solutions to verify them?

Substitute back into original

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