What is the first step in solving $$\frac{x}{x+4}=\frac{x}{10}$$ ?

Cross-multiply to get $$10x = x(x + 4)$$ .

What are the possible solutions for $$\frac{x}{x+4}=\frac{x}{10}$$ ?

The solutions are $$0$$ and $$6$$ .

How do you combine fractions with different denominators?

To combine fractions with different denominators, find the least common denominator, convert each fraction, and then add or subtract the numerators.

Solve for x: $$\frac{8}{x}=\frac{x}{18}$$ .

The solutions are $$-12$$ and $$12$$ .

What does it mean for a solution to be extraneous?

An extraneous solution is a solution that does not satisfy the original equation after substitution.

How can you check if your solution to a rational equation is correct?

Substitute the solution back into the original equation to verify that both sides are equal.

What is the importance of identifying restrictions in rational equations?

Identifying restrictions is important to avoid division by zero, which makes the equation undefined.

What is a common mistake when solving rational equations?

A common mistake is forgetting to check for extraneous solutions or not considering restrictions on the variable.

What is the general strategy for solving rational equations?

The general strategy includes finding the LCD, eliminating fractions, solving the resulting equation, and checking for extraneous solutions.

4.3 Solving Rational Equations Flashcard

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a rational equation?

Back

A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and/or denominator are polynomials.

2.

FLASHCARD QUESTION

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply the two fractions and set the products equal to each other.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

How do you isolate a variable in a rational equation?

Back

To isolate a variable, eliminate the fractions by multiplying both sides by the least common denominator (LCD) and then solve for the variable.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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