Complex Rational Expression: [1/a + 1/b] / [1/a^s - 1/b^2]

[silverdragon316]

The problem is:

1/a +1/b

1/a^2 - 1/b^2

1/a times b/b + 1/b times a/a
1/a^2 times b^2/b^2 - 1/b^2 times a^2/a^2

= b/ab+ a/ab
b^2/a^2b^2 - a^2/a^2b^2

=b+a/ab
b^2-a^2/a^2b^2

=(a+b)(a^2b^2)
ab(a^2-b^2)

=ab(a+b)(a+b)
ab(-ab)(a+b)

I worked it out and came up with:

a+b
-ab

is this correct?

 

[pka]

\(\displaystyle \L
\frac{{\frac{1}{a} + \frac{1}{b}}}{{\frac{1}{{a^2 }} - \frac{1}{{b^2 }}}} = \frac{{\left( {\frac{1}{a} + \frac{1}{b}} \right)\left( {a^2 b^2 } \right)}}{{\left( {\frac{1}{{a^2 }} - \frac{1}{{b^2 }}} \right)\left( {a^2 b^2 } \right)}} = \frac{{ab^2 + a^2 b}}{{b^2 - a^2 }}.\)

Can you finish?
Error fixed.

 

[silverdragon316]

Re: Complex Rational Expression

The problem is:

1/a +1/b

1/a^2 - 1/b^2

1/a times b/b + 1/b times a/a
1/a^2 times b^2/b^2 - 1/b^2 times a^2/a^2

= b/ab+ a/ab
b^2/a^2b^2 - a^2/a^2b^2

=b+a/ab
b^2-a^2/a^2b^2

=(a+b)(a^2b^2)
ab(a^2-b^2)

=ab(a+b)(a+b)
ab(-ab)(a+b)

I worked it out and came up with:

a+b
-ab

is this correct?

the bottom half of the problem is minus , you put plus.

 

[silverdragon316]

Re: Complex Rational Expression

The problem is:

1/a +1/b

1/a^2 - 1/b^2

1/a times b/b + 1/b times a/a
1/a^2 times b^2/b^2 - 1/b^2 times a^2/a^2

= b/ab+ a/ab
b^2/a^2b^2 - a^2/a^2b^2

=b+a/ab
b^2-a^2/a^2b^2

=(a+b)(a^2b^2)
ab(a^2-b^2)

=ab(a+b)(a+b)
ab(-ab)(a+b)

I worked it out and came up with:

a+b
-ab

is this correct?

I now came up with the answer

ab
a-b

is this correct? :?

 

[pka]

make it b-a

 

[skeeter]

I get ab/(b-a).