Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Expressions

How to add and subtract rational expressions: examples and their solutions.

Example 1

Simplify the given expression. 3/x + x/(x + 2)

Find the LCD (the LCM of the denominators):
x(x + 2).

Make both fractions's denominators to the LCD.

If there's a missing factor,
multiply the missing factor
to both of the numerator and the denominator.

Both fraction's denominators are the same.
So add these two fractions.

Example 2

Simplify the given expression. 2x/(x^2 - 1) + 5/(x^2 + x)

Find the LCD (the LCM of the denominators):
x(x + 1)(x - 1).

Factoring the difference of squares

Factoring using the distributive property

Make both fractions's denominators to the LCD.

Multiply the missing factor
to both of the numerator and the denominator.

Both fraction's denominators are the same.
So subtract these two fractions.