# Subtracting Algebraic Fractions – Examples and Practice

We can subtract two or more like algebraic fractions by using a single denominator and subtracting their numerators. If the algebraic fractions are unlike, we have to start by finding their least common denominator to write equivalent like fractions.

Here, we will look at some exercises on subtracting algebraic fractions. Also, we will explore practice problems to apply what we have learned.

##### ALGEBRA

Relevant for

Solving exercises of subtraction of algebraic fractions.

See examples

##### ALGEBRA

Relevant for

Solving exercises of subtraction of algebraic fractions.

See examples

## Examples with answers of subtraction of algebraic fractions

### EXAMPLE 1

Find the subtraction of the following fractions: $latex \frac{a}{b}-\frac{c}{b}$.

In this case, both fractions have the same denominator $latex b$. That is to say, we are dealing with two fractions with a common denominator $latex b$.

Since we are dealing with fractions with common denominator, the resulting fraction will be the subtraction of the numerators divided by the common denominator, which in this example is $latex b$.

$$\frac{a}{b} – \frac{c}{b} = \frac{a – c}{b}$$

The result is:

$$\frac{a – c}{b}$$

### EXAMPLE 2

Find the difference between $latex \frac{3x}{5}$ and the fraction $latex \frac{2x}{5}$.

We propose the operation to be performed:

$$\frac{3x}{5} – \frac{2x}{5}$$

We notice again that it is a subtraction of two fractions with a common denominator, 5.

The resulting fraction is obtained by subtracting the numerators and dividing by the common denominator:

$$\frac{3x}{5} – \frac{2x}{5} = \frac{3x – 2x}{5}$$

$$= \frac{x}{5}$$

The result is:

$$\frac{x}{5}$$

### EXAMPLE 3

Consider the algebraic fraction $latex \frac{2x}{y}$ and the algebraic fraction $latex \frac{x}{z}$. Find the fraction that results from the subtraction of the given fractions.

Unlike the previous exercises, the two given fractions have different denominators.

The least common denominator (LCD) of both is $latex yz$.

If we multiply the numerator and denominator of the first fraction by z we have a fraction equivalent to the original one:

$$\frac{2xz}{yz}$$

Similarly, multiplying the numerator and denominator of the second by y gives the equivalent fraction:

$$\frac{xy}{zy}$$

We subtract the equivalent fractions:

$$\frac{2xz}{yz} – \frac{xy}{zy}$$

Since $latex yz = zy$ the above expression is equivalent to: