Subtracting Rational Expressions

Subtracting Rational Expressions

We subtract rational expressions as we do rational numbers.

To subtract when the denominators are the same, subtract the numerators and keep the same denominator. Then simplify if possible.

Subtract $\frac{8}{x}-\frac{3}{x}$

$\frac{8}{x}-\frac{3}{x}=\frac{8-3}{x}=\frac{5}{x}$

To subtract rational expressions with different denominators:

a. Find the LCM of the denominators. This is the least common

denominator (LCD).

b. For each rational expression, find an equivalent expression with

the LCD. To do so, multiply by 1 using a symbol for 1 made up of

factors of the LCD that are missing from the original denominator.

c. Subtract the numerators. Write the difference over the LCD.

d. Simplify if possible.