Expert: Scott A Wilson - 1/24/2010

Question
ok so i had a problem like this (1/5x + 1/2x)(1/5x - 1/4).
i know that we have to distrubute and i get
1/25x - 1/20x + 1/10x - 1/8
so i know that i have to combine - 1/20x + 1/10x but i dont know how i am  supposed to do this.  

Answer
I would write it as (x/5 + x/2)(x/5 - 1/4).

Note that x is in the numerator of both terms in the left set of parenthesis.
Since 10 should be made into the common denomoninator, this would give us 2x/10 + 5x/10 = 7x/10.

To the other parenthesis, 20 is the common denominator, so it is ((4x-5)/20).

Now when we multiply (7x/10)((4x-5)/20), we get 7x(4x-5)/200.
Multiplying the numerator gives (28x²-35x)/20.

This can be broken into 7x²/5 - 7x/4 or 7x(4x-5)/200.


Do you really mean (x/5 + 1/2)(x/5 - 1/4)?
Again, get common denominators first and then multiply it out.

It is best to get the entire problem over one denominator before working it out.


Note that on what you gave, (1/5x + 1/2x)(1/5x - 1/4), the answer to that is
x²/25 + x²/10 - x/20 - x/8, but then the fractions would need to be combined.