Simplifying formulas » Simplifying fractional formulas  


Contents

1. Simplifying
2. Factorising
3. Adding and subtracting fractional formulas
4. Multiplying fractional formulas

1. Simplifying

Simplification can be done by dividing the numerator and denominator with the same number. See also fractions. Of course you can also divide with a factor with a variable in it.

Example

20x32 = 5x8 = 58x
2032x = 58x
3xy–6y = x–2 = –12x (with y ≠ 0)*
3(x + y)2(x + y) = 32 = 112 (with x–y)*
Important: 3 + x3x cannot be shortened!

* In the original fraction 3xy–6y there is no outcome for y = 0.
However, in the simplified fraction it is possible to fill in y = 0.
This should not be possible because of the original. For that reason you write between brackets that y ≠ 0.

In the example beneath it, x and y should not be added zero.

At 2032x = 58x it is not necessary to write (with x ≠ 0).
In the simplified fraction you also do not have an outcome when x = 0.

IMPORTANT: In the DWO you do not have to write for example (with x ≠ 0) behind your answers, the DWO will not understand!


2. Factorising

Sometimes you have to factorise the numerator or denominator to get a common factor with which you can divide.

Examples

7(x + y)35x + 35y = 7(x + y)35(x + y) = 735 = 15 (with x–y)
4x2 + 3x4x = x(4x + 3)4x = 4x + 34 with x ≠ 0)
x2 + 4x – 212x – 6 = (x – 3)(x + 7)2(x – 3) = x + 72 (with x ≠ 3)

Simplifying further
If you want, you can simplify the second and third example further. Watch out that the question is not 'write as one fraction'. Then you have to keep the fraction.
4x + 34 = x + 34  and  x + 72 = 12x + 312.


3. Adding and subtracting fractional formulas

To add fractions, the denominators of the fractions have to be the same.
So, if necessary, make the denominators equal first.

Examples

52x + 73x = 156x + 146x = 296x
35x + 7x2 = 610x + 35x210x = 6 + 35x210x
34 + x = 34 + 4x4 = 3 + 4x4
25x – 35 = 25x – 3x5x = 2 – 3x5x
6x – 4xy = 6yxy – 4x2xy = 6y – 4x2xy
1x2y – 2xy2 = yx2y2 – 2xx2y2 =  y – 2xx2y2
3x205x2 = 3x3x2 + 4 x2 = 3x3 + 4x2
2x + 1 – 5xx + 2 = 2(x + 2)(x + 1)(x + 2) – 5x(x + 1)(x + 1)(x + 2) = 2(x + 2) – 5x(x + 1)(x + 1)(x + 2) =
2x + 4 – 5x2 – 5x(x + 1)(x + 2) = – 5x2 – 3x + 4(x + 1)(x + 2)  




4. Multiplying fractional formulas

When multiplying fractions, you always have to do numerator × numerator and denominator × denominator. Often you have to simplify after you multiplied.

Examples

2x × 5x4 = 10x4x = 212 (with x ≠ 0)
4yx × 32x = 12y2x2 = 6yx2


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