Question 1

Solve the equation $$\frac{x}{x+2} = \frac{3}{2}$$ algebraically. What is the solution?

Accepted Answer

$$x = -6$$

Question 2

When solving $$\frac{x}{x+2} = \frac{3}{2}$$, what is the least common multiple (LCM) of the denominators used to clear fractions?

Accepted Answer

$$2(x+2)$$

Question 3

Given the equation $$\frac{x}{x-2} - \frac{2}{x+1} = \frac{3}{x-2}$$, what is the LCM of the denominators?

Accepted Answer

$$(x-2)(x+1)$$

Question 4

Solve $$\frac{x}{x-2} - \frac{2}{x+1} = \frac{3}{x-2}$$ for $$x.$$

Accepted Answer

$$x = 4$$

Question 5

After clearing denominators in $$\frac{x}{x-2} - \frac{2}{x+1} = \frac{3}{x-2}$$, what is the resulting equation?

Accepted Answer

$$x(x+1) - 2(x-2) = 3(x+1)$$

Question 6

Solve the equation $$\frac{x}{x+4} - \frac{3}{4} = \frac{4}{x^2$-16}$$ for $$x.$$

Accepted Answer

No solution

Question 7

Why is $$x = 4$$ not a solution to $$\frac{x}{x+4} - \frac{3}{4} = \frac{4}{x^2$-16}$$?

Accepted Answer

It makes the denominator zero

Question 8

Which of the following is a necessary step when solving rational equations like $$\frac{x}{x+2} = \frac{3}{2}$$?

Accepted Answer

Multiply both sides by the LCM of the denominators

Question 9

If you solve a rational equation and find $$x = 2$$, but $$x = 2$$ makes a denominator zero in the original equation, what should you do?

Accepted Answer

Reject $$x = 2 as an $$extraneous solution

Question 10

In the context of rational equations, what is an extraneous solution?

Accepted Answer

A solution that makes any denominator zero

Question 11

Which real-world scenario could be modeled by a rational equation similar to $$\frac{x}{x+2} = \frac{3}{2}$$?

Accepted Answer

Mixing solutions with different concentrations

Question 12

If $$x = -2 is $$found as a solution to $$\frac{x}{x+2} = \frac{3}{2}$$, what should you conclude?

Accepted Answer

$$x = -2 is $$not a solution because it makes the denominator zero

Solving Rational Equations Algebraically

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