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

If x = 0, (x – 5)2 = 25 and (x + 5)2 = 25, so the quantities are equal.

If x = 1, (x – 5)2 = (–4)2 = 16 and (x + 5)2 = 62 = 36, so B is greater.

This is a contradiction, so the answer cannot be determined.

To solve this problem, first multiply each term of the original expression by the denomenator of the other over itself:

Then you will have two terms with a common denomenator:

Combine the terms and 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:

The answer is 7.

Write two independent equations that represent the problem.

x + y = 17 and 12_x_ + 7_y_ = 169

If we solve the first equation for x, we get x = 17 – y and we can plug this into the second equation.

12(17 – y) + 7_y_ = 169

204 – 12_y_ + 7_y_ =169

–5_y_ = –35

y = 7

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.

To add rational expressions, first find the least common denominator. Because the denominator of the first fraction factors to 2(x+2), it is clear that this is the common denominator. Therefore, multiply the numerator and denominator of the second fraction by 2.

This is the most simplified version of the rational expression.

To simplify the following, a common denominator must be achieved. In this case, the first term must be multiplied by (x+2) in both the numerator and denominator and likewise with the second term with (x-3).

The answer is 98.

If the area of each square tile is 49 then each side of the tile is 7. The width of the floor is 98 so 14 tiles would fit across. The length of the floor is 49 so 7 tiles would fit down.

14 tiles * 7 tiles = 98 tiles total

To simplify this expression, you have to get both numerators over a common denominator. The best way to go about doing so is to multiply both expressions by the others denominator over itself:

Then you are left with:

Which you can simplify into:

From there, you can take out a :

Which gives you your final answer:

To solve this problem, first multiply both terms of the expression by the denominator of the other over itself:

Now that both terms have a common denominator, you can add them together:

To simplify, first multiply both terms by the denominator of the other term over itself:

Then, you can combine the terms, now that they share a denominator:

We will need to simplify the expression . We can think of this as a large fraction with a numerator of and a denominator of .

In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator. has a denominator of , and has a denominator of . The least common denominator that these two fractions have in common is . Thus, we are going to write equivalent fractions with denominators of .

In order to convert the fraction to a denominator with , we will need to multiply the top and bottom by .

Similarly, we will multiply the top and bottom of by .

We can now rewrite as follows:

=

Let's go back to the original fraction . We will now rewrite the numerator:

=

To simplify this further, we can think of as the same as . When we divide a fraction by another quantity, this is the same as multiplying the fraction by the reciprocal of that quantity. In other words, .

=

Lastly, we will use the property of exponents which states that, in general, .

The answer is .

Multiply by the reciprocal of .

Factor

Divide by common factors.

To tackle this problem, you need to invert and multiply:

Here we see that we have created a quadratic equation. Therefore, we get all terms to one side, set it equal to zero and use the quadratic formula to solve.

The quadratic formula is:

where

Plugging these values in we get the following:

To divide one rational expression by another, invert and multiply:

Remember to foil the numerator meaning, multiply the first components of each binomial. Then multiply the outer components of each binomial. After that, multiply the inner components together, and lastly, multiply the components in the last position of the binomials together.

This arrives at the following:

You can't factor anything out, so that's your final answer.