Simplify these expressions?

Question

1. 1/x-1 + 2/x-2 + 1/x-3 (three fractions in the expression)
2. 1/x+y - 1/x-y + 2x/x^2-y^2 (again, three fractions)
3. 3/x^2+x-2 - 5/x^2-x-6 (three fractions)

Thanks!

singing, the answer to 1 in the book is 2 over (x-1)(x-2)(x-3). I did it your way earlier, and got the same answer, but is there anyway I can derive a fractional answer from that?

Answer 1

In all these expressions, it is necessary to find common denominators first. For number 1:
multiply the first term by (x-2)(x-3)/(x-2)(x-3)
multiply the second term by (x-1)(x-3)/(x-1)(x-3)
mult the third term by (x-1)(x-2) / (x-1)(x-2)
then add and simplify the numerators. Then reduce.

For the second problem : The denominator of the third term is (X-y)(x+y). Mult first by (x-y) / (x-y) mult the second by (x+y) / (x+y).
Add numerators and simplify.

For the third, the denominator of the first term is (x+2)(x-1).
The denom of the second term is (x-3)(x+2).
Do the same thing as above --- make 'em the same.

Answer 2

1. 1/(x-1)+2(x-2)+1/(x-3)=
[(x-2)(x-3)+2(x-1)(x-3)+(x-1)(x-2)]/(x-1)(x-2)(x-3)=
[2x^2-8x+7]/(x-1)(x-2)(x-3)
2. 1/(x+y)-1/(x-y)+2x/(x^2-y^2)=
[x-y-x-y+2x]/(x^2-y^2]=
2/(x+y)
3. I can only see two fractions?
3/(x^2+x-2)-5/(x^2-x-6)=
[3(x-3)-5(x-1)]/(x-1)(x+2)(x-3)=
[3x-5x-9+5]/(x-1)(x+2)(x-3)=
-2/(x-1)(x-3)

Singing where did you get 11 as the c part of the numerator? I thought it was 14.

Answer 3

1. Simplify: (1/x-1)+(2/x-2)+(1/x-3)

First: eliminate fractions - multiply the denominators by each term...

(x-1)(x-2)(x-3)(1/x-1)+(x-1)(x-2)(x-3)(2/x-2)+(x-1)(x-2)(x-3)(1/x-3)

Sec: cross cancel "like" terms & combine the remaining terms...

(x-2)(x-3)(1)+(x-1)(x-3)(2)+(x-1)(x-2)(1)
(x-2)(x-3)+(x-1)(x-3)(2)+(x-1)(x-2)

*Use the Foiling Method...

x^2-3x-2x+6+2(x^2-3x-x+3)+x^2-2x-x+2
x^2-3x-2x+6+2x^2-6x-2x+3)+x^2-2x-x+2
x^2 - 5x + 6 + 2x^2 - 8x + 3 + x^2 - 3x + 2

Third: combine "like" terms...

x^2 + x^2 + 2x^2 - 5x - 8x - 3x + 6 + 3 + 2

= 4x^2 - 16x + 11

P.S. Follow the same format & try the rest.

Answer 4

1( . ) + 1( . )= 2 Big Fake Boobs!