Algebra : Join Fractions

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The join fractions command essentially does the reverse of the partial fractions command, attempting to write sums and differences of fractions as a single fraction. It will put terms in a sum or difference over a common denominator which is usually the lowest common multiple of the denominators of each of the individual terms.

To use the join fractions command, simply go to the basic join fractions page, type in your expression and hit the "Join Fractions" button. Your question will be automatically answered by computer and the reply will be shown in your browser within a few seconds. If you would like more control over how your question is answered, try the advanced join fractions page, where there are a number of options which allow you to customize the command.


Here are some examples illustrating the types of expressions you can use the join fractions command on and the results which QuickMath will return.

 Basic join fractions command
Expression Result

2 x
1 + x + 5 x
 x  (1 + x)

b c + a d
   b d

 1 + 2 a
a (1 + a)

 Advanced join fractions command

Expression Option Result
1/(1+sin(x))+1/cos(x) Trig

1 + sec(x) + tan(x)
    1 + sin(x)
(2x^2+2)/(8x+i) Modulo 7 -2 i + 2 x
(x^2-3)/(x-sqrt(3)) Automatic
sqrt(x) + 3

Options (advanced page only)

Trig functions

Values : checked or unchecked
Default : unchecked

When Trig functions is checked, the join fractions command will treat trigonometric functions as rational functions of exponentials and manipulate them accordingly.


Values : checked or unchecked + empty string or prime number or zero
Default : unchecked + empty string

When Modulo is checked and an integer n is entered into the modulo field, the calculations are carried out over the field of integers modulo n. When Modulo is unchecked or the text field contains 0 or is empty, the calculations are carried out over the field of integers.

Field extensions

Values : none or automatic or custom + custom extension expressions (only if the custom option is selected)
Default : none

Choosing the none option means that the calculations will be carried out over the field of integers (default).

Choosing the automatic option will extend the field over which the calculations are performed by any algebraic numbers appearing in the expression.

Choosing the custom option enables you to choose your own field extensions.