Fractions:Simplifying Fractions

[afvatcha]

FDP Strategy Guide pg. 39, #6 2007 edition.

Simplify 10x/5+x

Answer: Cannot be simplified.

My question is why can't you simplify in this case? Is it because the numerator is multiplying the variable and the denominator is adding the variable?

If it was 10+x/5+x could you simplifiy?
or more obviously,
10x/5x could you simplify?

Sorry if this is a simple question.

[Ben Ku]

Hi,

You can never simplify a fraction with terms that are added or subtracted from each other. You can only simplify things that are multiplied together.

For example,
10 / 5 = (2*5)/(5) = 2
10x/5x = (2*5*x)/(5*x) = 2
(x - 2)(x + 2)/(x - 2) = x + 2

However, you cannot simplify these:
10 / (x + 5)
(x + 10) / (x + 5)

Let me know if you have any questions about this.

[Kweku.Amoako]

Hi bku,

when do u advice to use the conjugate to simplify?

[Ben Ku]

Hi kweko,

If you have an expression a + b, then the conjugate is a - b. The only place you'll need to use the conjugate is if you have a square root in the denominator.

For example,

To simplify 4 / (2 + sqrt(3))
you should multiply the numerator and denominator by (2 - sqrt 3) to get rid of the square root in the denominator

[4(2 - sqrt(3))] / [(2 + sqrt(3))(2 - sqrt(3))] = [4 - 4 sqrt(3)] / [4 - 3] = 4 - 4 sqrt (3).

Hope that helps.