### All GRE Math Resources

## Example Questions

### Example Question #1 : Rational Expressions

If √(*ab*) = 8, and *a*^{2 }= *b*, what is *a*?

**Possible Answers:**

4

2

64

16

10

**Correct answer:**

4

If we plug in *a*^{2} for *b* in the radical expression, we get √(*a*^{3}) = 8. This can be rewritten as *a*^{3/2} = 8. Thus, log* _{a }*8 = 3/2. Plugging in the answer choices gives 4 as the correct answer.

### Example Question #1 : How To Evaluate Rational Expressions

**Possible Answers:**

–37/15

37/15

–9/5

–11/5

9/5

**Correct answer:**

–11/5

### Example Question #1 : Rational Expressions

Find the product of and .

**Possible Answers:**

**Correct answer:**

Solve the first equation for .

Solve the second equation for .

The final step is to multiply and .

### Example Question #1 : How To Evaluate Rational Expressions

Evaluate the following rational expression, if :

**Possible Answers:**

**Correct answer:**

To evaluate, simply plug in the number for :

Remembering to use order of operations (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) we arrive at our final solution.

### Example Question #2 : How To Evaluate Rational Expressions

If , find .

**Possible Answers:**

**Correct answer:**

To solve, simply plug in for :

Remembering to use the correct order of operations (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) we arrive at our final answer.

First do the multiplication that is in the numerator.

Now do the subtraction in the denominator.

### Example Question #3 : How To Evaluate Rational Expressions

Find if .

**Possible Answers:**

**Correct answer:**

To solve, simply plug in for :

Remembering to use the correct order of operations (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) we arrive at the final solution.

Also recall that when a negative number is squared it becomes a positive number. This is also true when we multiply two negative numbers together.

### Example Question #4 : How To Evaluate Rational Expressions

Evaluate if .

**Possible Answers:**

**Correct answer:**

To evaluate, merely plug in for :

Remembering order of operations (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) we arrive at our final solution.

From here we can further reduce the fraction by factoring out a two from both the numerator and denominator.

Canceling out the two's we get:

### Example Question #5 : How To Evaluate Rational Expressions

Evaluate if .

**Possible Answers:**

**Correct answer:**

To solve, simply plug in for :

Recall that when a negative number is divided by another negative number it results in a positive number.

### Example Question #6 : How To Evaluate Rational Expressions

Evaluate if .

**Possible Answers:**

**Correct answer:**

To evaluate, simply plug in for :

Remembering the order of operations (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) we arrive at our final solution.

### Example Question #7 : How To Evaluate Rational Expressions

Evaluate if .

**Possible Answers:**

**Correct answer:**

To solve, simply plug in for :

Remembering the order of operations (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) we arrive at our final solution. Also recall that multiplying two negative numbers together leads to a positive product; this is also true when you square a negative number.

From here we can reduce the fraction by factoring out a four from both the numerator and the denominator.