## Algebra 1

Adding and Subtracting Rational Expressions is much like adding and subtracting normal fractions. 1) You must always have a common denominator in order to add or subtract. 2) If you do not have a common denominator, you need to find the Least Common Denominator, or the LCM (Least Common Multiple). You can find this by listing out the factors of each denominator. 3) Once you have a common denominator, you use it to rewrite each fraction. 4) Now all that is left is to add or subtract the numerators and put it over your common denominator! Example: To solve: $\frac{4}{6b^2} + \frac{5}{8b^3}$, you will first need to make sure both fractions have common denominators. To do this, we must find the LCD, or the Least Common Multiple, by writing out each as products of prime factors. $6b^2 = 2 \times 3 \times b \times b$ $8b^3 = 2 \times 2 \times 2 \times b \times b\times b$ The Least Common Multiple, or LCD, then is $2\times 2\times 2\times 3\times b\times b\times b = 24b^3$ Now\times we can rewrite the fractions using the new LCD we found. $\frac{4}{6b^2} + \frac{5}{8b3}$ = $\frac{4\times 2\times 2\times b}{6b^2 \times 2 \times 2 \times b} + \frac{5 \times3}{8b^3 \times 3}$ =$\frac{16b}{24b^3} + \frac{15}{24b^3}$ Now that we have common denominators, we can add the numerators: $\frac{16b}{24b^3} + \frac{15}{24b^3}$ = $\frac{16b + 15}{24b^3}$