GRE Math : How to evaluate rational expressions

Study concepts, example questions & explanations for GRE Math

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Example Questions

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Example Question #3 : Rational Expressions

If √(ab) = 8, and a= b, what is a?

Possible Answers:

4

64

10

2

16

Correct answer:

4

Explanation:

If we plug in a2 for b in the radical expression, we get √(a3) = 8. This can be rewritten as a3/2 = 8. Thus, loga 8 = 3/2. Plugging in the answer choices gives 4 as the correct answer. 

Example Question #2 : Rational Expressions

Function_part1

 

Possible Answers:

–37/15

9/5

37/15

–11/5

–9/5

Correct answer:

–11/5

Explanation:

Fraction_part2

Fraction_part3

Example Question #1 : How To Evaluate Rational Expressions

Find the product of  and .

Possible Answers:

Correct answer:

Explanation:

Solve the first equation for .


Solve the second equation for

The final step is to multiply  and .

      

 

Example Question #21 : Expressions

Evaluate the following rational expression, if :

Possible Answers:

Correct answer:

Explanation:

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 #22 : Expressions

If , find .

 

Possible Answers:

Correct answer:

Explanation:

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 #23 : Expressions

Find  if .

 

Possible Answers:

Correct answer:

Explanation:

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 #24 : Expressions

Evaluate  if .

Possible Answers:

Correct answer:

Explanation:

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 #25 : Expressions

Evaluate  if .

Possible Answers:

Correct answer:

Explanation:

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 #26 : Expressions

Evaluate  if .

Possible Answers:

Correct answer:

Explanation:

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 #27 : Expressions

Evaluate  if .

Possible Answers:

Correct answer:

Explanation:

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.

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