### All High School Math Resources

## Example Questions

### Example Question #1 : Understanding Rational Expressions

Solve:

If varies directly as , and when , find when .

**Possible Answers:**

**Correct answer:**

The formula for a direct variation is:

Plugging in our values, we get:

### Example Question #2 : Understanding Rational Expressions

If two boxes have the same depth and capacity, the length is inversely proportional to the width. One box is long and wide. A second box (same depth and capacity) is long. How wide is it?

**Possible Answers:**

**Correct answer:**

The formula for an indirect variation is:

Plugging in our values, we get:

### Example Question #1 : Simplifying Rational Expressions

Simplify

**Possible Answers:**

**Correct answer:**

This is a more complicated form of

Find the least common denominator (LCD) and convert each fraction to the LCD, then add the numerators. Simplify as needed.

which is equivalent to

Simplify to get

### Example Question #2 : Simplifying Rational Expressions

Divide and simplify the following rational expression:

**Possible Answers:**

**Correct answer:**

Multiply by the reciprocal of the second expression:

Factor the expressions:

Remove common terms:

### Example Question #3 : Simplifying Rational Expressions

Add and simplify the following rational expression:

**Possible Answers:**

**Correct answer:**

Begin by multiplying the left term by :

Simplify:

### Example Question #4 : Simplifying Rational Expressions

Simplify the following rational expression:

**Possible Answers:**

**Correct answer:**

Begin by combining the terms in the denominator:

Multiply by the reciprocal of the denominator:

Remove like terms:

### Example Question #5 : Simplifying Rational Expressions

Simplify the following rational expression:

**Possible Answers:**

**Correct answer:**

Create a common denominator of in both the numerator and denominator:

Multiply by the reciprocal of the denominator:

Simplify:

Remove common terms:

### Example Question #6 : Simplifying Rational Expressions

Multiply and simplify the following rational expression:

**Possible Answers:**

**Correct answer:**

Factor the expression:

Remove like terms:

### Example Question #7 : Simplifying Rational Expressions

Divide and simplify the following rational expression:

**Possible Answers:**

**Correct answer:**

Multiply by the inverse of the denominator:

Factor:

Remove like terms:

### Example Question #1 : Solving Rational Equations And Inequalities

Solve the following rational expression:

**Possible Answers:**

**Correct answer:**

Multiply the equation by :

Certified Tutor