# Thread: algebraic fraction 2

1. ## algebraic fraction 2

Can any one help with two problems I have

x/xy+x^2 + y/x^2+xy =x/y(x+y) +y/x(x+y)=x^2/xy(x+y)+y^2/xy(x+y)=x^2+y^2/xy(x+y)

with this ome I can work out why xy(x+y) s the common factor and why the x and th Y become squared.

1/x^2+x - 1/x+1 = 1/x(x+1) -x/x(x+1)

with this one why does the x appear as a numerator

hope this all makes sence.

many thanks

Dave

2. ## Re: algebraic fraction 2

Originally Posted by davellew69
Can any one help with two problems I have

x/xy+x^2 + y/x^2+xy =x/y(x+y) +y/x(x+y)=x^2/xy(x+y)+y^2/xy(x+y)=x^2+y^2/xy(x+y)

with this ome I can work out why xy(x+y) s the common factor and why the x and th Y become squared.

1/x^2+x - 1/x+1 = 1/x(x+1) -x/x(x+1)

with this one why does the x appear as a numerator

hope this all makes sence.

many thanks

Dave
because ...

$\displaystyle \frac{1}{x+1} \cdot \frac{x}{x} = \frac{x}{x(x+1)}$

next time, use grouping symbols to collect terms in the numerator and denominator of your fractions

for example, x/xy+x^2 could be misinterpreted as $\displaystyle \frac{x}{xy} + x^2$ , so write it as x/(xy+x^2)

3. ## Re: algebraic fraction 2

thanks for the reply but I m lost on what your reply was trying to say

dave

4. ## Re: algebraic fraction 2

Originally Posted by davellew69
thanks for the reply but I m lost on what your reply was trying to say

dave
you originally asked ...

1/x^2+x - 1/x+1 = 1/x(x+1) -x/x(x+1)
with this one why does the x appear as a numerator
I answered your question ... note that the common denominator of the two fractions is x(x+1).

5. ## Re: algebraic fraction 2

The "1/x(x+1) - x/x(x+1)" in previous post needs further bracketing:
1 / [x(x+1)] - x / [x(x+1)]

Your starting expression should be shown this way:
1 / (x^2 + x) - 1 / (x + 1) ; then:

= 1 / [x(x + 1)] - 1 / (x + 1)

= 1 / [x(x+1)] - x / [x(x+1)]

= (1 - x) / [x(x + 1)]

6. ## Re: algebraic fraction 2

Originally Posted by davellew69
x/xy+x^2 + y/x^2+xy =x/y(x+y) +y/x(x+y)=x^2/xy(x+y)+y^2/xy(x+y)=x^2+y^2/xy(x+y)
Dave, that's quite messy; if you don't show proper bracketing, then I don't think we should
lose our time trying to decipher what you mean. Your original expression "x/xy+x^2 + y/x^2+xy"
MUST be shown this way:
x / (xy + x^2) + y / (x^2+xy) ; and

x / (xy + x^2) = x / [x(x + y)] , not x / [y(x + y)] as you have...

For your benefit:
20 / (2 + 3) = 20 / 5 = 4
20 / 2 + 3 = 10 + 3 = 13
See the importance of proper bracketing?

### algebraic fraction2

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