Rational Expressions - GRE Quantitative Reasoning

Factor first. The numerators will not factor, but the first denominator factors to (x – 2)(x + 2) and the second denomintaor factors to x(x – 2). Multiplying fractions does not require common denominators, so now look for common factors to divide out. There is a factor of x and a factor of (x + 2) that both divide out, leaving 4 in the numerator and two factors of (x – 2) in the denominator.

6/8 X 20/3 first step is to reduce 6/8 -> 3/4 (Divide top and bottom by 2)

3/4 X 20/3 (cross-cancel the threes and the 20 reduces to 5 and the 4 reduces to 1)

1/1 X 5/1 = 5

When multiplying two binomials, it's best to remember the mnemonic FOIL, which stands for First, Outer, Inner, and Last. Going in the order of FOIL, we multiply the first term of each binomial, then the outer terms of the expression, then the inner terms of the expression, and finally the last term of each binomial. For this question we get: Now that we have 'FOILed' our expression, we simply add our results to get the final answer.

To do this problem, simply multiply as you would with any fraction, combining like terms whenever possible:

When multiplying, make sure to distribute through to all terms in the polynomial.

Then you can factor out a six to simplify for your final answer:

Since both expressions have a common denominator, x2, we can just recopy the denominator and focus on the numerators. We get (9x - 2) - (6x - 8). We must distribute the negative sign over the 6x - 8 expression which gives us 9x - 2 - 6x + 8 ( -2 minus a -8 gives a +6 since a negative and negative make a positive). The numerator is therefore 3x + 6.

Since both fractions in the expression have a common denominator of , we can combine like terms into a single numerator over the denominator:

Since both rational terms in the expression have the common denominator , combine the numerators and simplify like terms:

Since both terms in the expression have the common denominator , combine the fractions and simplify the numerators:

When adding rational expressions with common denominators, you simply need to add the like terms in the numerator.

Therefore, is the best answer.

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.

Solve the first equation for .

Solve the second equation for .

The final step is to multiply and .

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.

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.

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.

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:

To solve, simply plug in for :

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

To evaluate, simply plug in for :

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

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.

To evaluate, simply plug in for :

Remembering the order of operations we are able to solve this problem. The order of operations is parentheses, exponents, multiplication, division, addition, subtraction.