# ACT Math : How to add rational expressions with a common denominator

## Example Questions

### Example Question #2421 : Act Math

Compute the following:

Explanation:

Notice that the denominator are the same for both terms. Since they are both the same, the fractions can be added. The denominator will not change in this problem.

### Example Question #1 : How To Add Rational Expressions With A Common Denominator

Simplify the following rational expression: (9x - 2)/(x2) MINUS (6x - 8)/(x2)

Explanation:

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.

### Example Question #1 : How To Add Rational Expressions With A Common Denominator

Simplify the following rational expression:

Explanation:

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

### Example Question #3 : How To Add Rational Expressions With A Common Denominator

Simplify the following expression:

Explanation:

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

### Example Question #1 : How To Add Rational Expressions With A Common Denominator

Simplify the following rational expression:

Explanation:

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

### Example Question #2426 : Act Math

Combine the following rational expressions: