# High School Math : Rational Expressions

## Example Questions

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### Example Question #1 : Understanding Rational Expressions

Solve:

If varies directly as , and  when , find when .

Explanation:

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?

Explanation:

The formula for an indirect variation is:

Plugging in our values, we get:

### Example Question #1 : Simplifying Rational Expressions

Simplify

Explanation:

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:

Explanation:

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:

Explanation:

Begin by multiplying the left term by :

Simplify:

### Example Question #4 : Simplifying Rational Expressions

Simplify the following rational expression:

Explanation:

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:

Explanation:

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:

Explanation:

Factor the expression:

Remove like terms:

### Example Question #7 : Simplifying Rational Expressions

Divide and simplify the following rational expression:

Explanation:

Multiply by the inverse of the denominator:

Factor:

Remove like terms:

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

Solve the following rational expression: