Algebraic Fractions and Equations
Algebraic Fractions: Part 1

When fractions are added or subtracted, a common denominator must be used as shown below:

+ = +
=

When working with algebraic fractions a similar approach must be used.

Worked Examples

1

Express

+

as a single fraction.

Show me

These fractions should be added by using a common denominator of 30.

+ = +
=
2

Express

+

as a single fraction.

Show me

In this case, the common denominator will be x(x + 1).

Using this gives

+ = +
= +
=
3

Express

+

as a single fraction.

Show me

In this case, the common denominator will be (2x + 1) (x + 1).

Using this gives

+ = +
= +
=

Exercises

Simplify each expression into a single fraction.

(a)
+ =
(b)
+ =
(c)
+ =
(d)
+ =
(e)
+ =
(f)
+ =
(g)
− =
(h)
− =
(i)
+ =
(j)
+ =
(k)
+ =
(l)
+ =
(m)
− =
(n)
+ =
(o)
− =

Express the following as single fractions.

(a)
+ =
(b)
− =
(c)
+ =
(d)
− =
(e)
+ =
(f)
− =
(g)
+ =
(h)
− =
(i)
− =
(j)
− =
(k)
− =
(l)
− =

Combine the fractions below into a single fraction.

(a)
+ =
(b)
+ =
(c)
+ =
(d)
− =
(e)
− =
(f)
− =
(g)
− =
(h)
+ =
(i)
+ =
(j)
+ =
(k)
+ =
(l)
+ =

Simplify each expression.

(a)
+ =
(b)
− =
(c)
+ =
(d)
+ =
(e)
+ =
(f)
+ =
(g)
− =
(h)
− =
(i)
− =

Write as a simple fraction in LOWEST terms

+

Simplify −