# SAT Math : Expressions

## Example Questions

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### Example Question #1 : Rational Expressions

Simplify the expression.

Explanation:

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.

### Example Question #1 : Rational Expressions

Simplify the following:

Explanation:

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).

### Example Question #2 : Rational Expressions

If √(ab) = 8, and a= b, what is a?

4

16

64

10

2

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.

–11/5

–37/15

9/5

–9/5

37/15

–11/5

Explanation:

### Example Question #5 : Rational Expressions

If Jill walks  in , how long will it take Jill to walk

Explanation:

To solve this, we need to set a proportion.

Cross Multiply

So it will take Jill  to walk

### Example Question #1 : Expressions

If , then which of the following must be also true?

Explanation:

### Example Question #1 : Rational Expressions

Which of the following is equivalent to  ? Assume that denominators are always nonzero.

Explanation:

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, .

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

Simplify (4x)/(x– 4) * (x + 2)/(x– 2x)

(4x+ 8x)/(x+ 8x)

x/(x – 2)2

4/(x – 2)2

x/(x + 2)

4/(x + 2)2

4/(x – 2)2

Explanation:

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.

### Example Question #1 : Rational Expressions

what is 6/8 X 20/3

18/160
3/20
9/40
5
120/11
Explanation:

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

### Example Question #9 : Rational Expressions

Evaluate and simplify the following product: