Add -5/(x-1)+(2-x)/x

In order to add fractions, they must have common
denominators.  The common denominator in this case is the product of the two given
denominators.  Therefore, the common denominator is x(x -
1).

Multiply the first fraction by
x.

-5 / (x - 1) = -5x / x(x -
1)

Multiply the second fraction by (x -
1)

(2 - x)(x - 1) / x(x -
1)

Now that the fractions have common denominators, you are
able to add their numerators.

numerator:  -5x + (2 - x)(x -
1)

denominator:  x(x -
1)

Multiply the binomials in the numerator using
FOIL.

-5x + 2x - 2 - x^2 +
x

Combine like terms.

-x^2 -
2x - 2

Use the distributive property in the
denominator.

x(x - 1)

x^2 -
x

To avoid negative coefficients, multiply everything by
-1.

numerator:  -1(-x^2 - 2x - 2) = x^2 + 2x +
2

denominator:  -1(x^2 - x) = -x^2 + x = x -
x^2

Simplify the denominator by factoring out the
x.

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

So now
you have this:

numerator:  x^2 + 2x +
2

denominator:  x(1 -
x)

Simplified answer:  (x^2 + 2x + 2) / [x(1
- x)]