Question 1153848

{{{-2/(x^2-4) + (x-1)/(x^2-2x)}}}

 1: What is the problem?  What do you need to find or do ? What will your final answer look like?

we have to find the sum of two rational expressions
first, we need to factor denominators  and , then find common denominator 
final answer will look like one rational expression

2: What have they told you? What does it mean? What more do you know or can you figure out? What connections can you make?

We can add  rational expressions in much the same way as we add  numerical fractions.
To add  rational expressions with unlike denominators, first find the LCM of the denominator, write each expression using the LCD, add the numerators, and simplify as needed.

3: Solve by showing steps towards completing the problem, including writing/using equations.

{{{-2/(x^2-4) + (x-1)/(x^2-2x)}}}


factor denominator:

 {{{(x^2-4) =(x-2)(x+2)}}}
and 
{{{(x^2-2x)=x(x-2)}}}


=> common denominator is {{{x(x-2)(x+2)}}}


{{{-2x/(x(x-2)(x+2)) +( (x-1)(x+2))/(x(x-2)(x+2))}}}


{{{(-2x + x^2 + x - 2)/(x(x-2)(x+2))}}}


{{{(  x^2 -x - 2)/(x(x-2)(x+2))}}}


{{{(  (x + 1) (x - 2))/(x(x-2)(x+2))}}}........simplify


{{{(  (x + 1) cross((x - 2)))/(x*cross((x-2))(x+2))}}}


{{{  (x + 1) /(x(x+2))}}}


4: final answer


{{{  (x + 1) /(x(x+2))}}}