# ACT Math : Expressions

## Example Questions

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### Example Question #2462 : Sat Mathematics

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 #1 : Expressions

Simplify the following

Explanation:

Find the least common denominator between x-3 and x-4, which is (x-3)(x-4). Therefore, you have .  Multiplying the terms out equals . Combining like terms results in .

### Example Question #1 : Expressions

Simplify the following expression:

Explanation:

In order to add fractions, we must first make sure they have the same denominator.

So, we multiply  by  and get the following:

Then, we add across the numerators and simplify:

### Example Question #2391 : Act Math

Combine the following two expressions if possible.

Explanation:

For binomial expressions, it is often faster to simply FOIL them together to find a common trinomial than it is to look for individual least common denominators. Let's do that here:

FOIL and simplify.

Combine numerators.

Thus, our answer is

### Example Question #1 : Expressions

Select the expression that is equivalent to

Explanation:

To add the two fractions, a common denominator must be found. With one-term denominators, it is easier to simply find the least common denominator between them and multiply each side to obtain it.

In this case, the least common denominator between  and  is . So the first fraction needs to be multiplied by  and the second by :

Now, we can add straight across, remembering to combine terms where we can.

So, our simplified answer is

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

Find the product of  and .

Explanation:

Solve the first equation for .

Solve the second equation for

The final step is to multiply  and .

### Example Question #1 : Rational Expressions

The following table shows the temperature of a cup of coffee at different times

Time                           1:09    1:11    1:13    1:15    1:17

Temperature (ºF)            187.1  184.4  181.7  179.0  176.3

If this trend continues, what will the temperature of the coffee at minute 1:25?

162.9°F

160.2°F

168.3°F

171.0°F

165.5°F

165.5°F

Explanation:

The table shows that for every two minutes, the temperature of the coffee lowers 2.7ºF. At 1:25, 16 minutes, or eight 2-minute intervals have passed, and the temperature of the coffee has lowered by 8*2.7ºF, reaching a temperature of 165.5ºF.

### Example Question #8 : Expressions

Amy buys concert tickets for herself and her friends. She initially buys them at $40/ticket. Weeks later, her other friends ask her to buy them tickets, but the prices have increased to$54. Amy buys 7 tickets total and spends $350. How many tickets has she paid$40 on?

Explanation:

Amy has bought 7 tickets, x of them at $40/ticket, and the remaining 7-x at$54/ticket. She spends at total of

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

What is

?

Explanation:

To find an equivalency we must rationalize the denominator.

To rationalize the denominator multiply the numerator and denominator by the denominator.

To simplify completely, factor out a three from the numerator and denominator resulting in the final solution.

### Example Question #1 : Rational Expressions

Simplify:

Explanation:

The common denominator of these two fractions simply is the product of the two denominators, namely:

Thus, you will need to multiply each fraction's numerator and denominator by the opposite fraction's denominator:

Let's first simplify the numerator:

, which is the simplest form you will need for this question.

However, the correct answer has the denominator multiplied out. Merely FOIL

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