How do you solve x+1/x(x-1) - 1/2(x-1)

Question

x+1          1

----    -  -------

x(x-1)    2(x-1)

Answer 1

Since we are subtracting fractions with uncommon denominators, we need to find the LCD.  The LCD is 2x(x - 1).

 

 

[2(x + 1) - x] / [2x(x - 1)] =

 

 

Simplify the numerator.

 

(2x + 2 - x) / (2x(x - 1)) =

 

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

 

 

 

 

 

Answer 2

(x+1)/[x(x-1)] - 1/[2(x-1]

 

We need to find a common denominator... get the same equation

on the bottom of both fractions so that we can add them together

(or subtract...)

 

The denominator on 1st is x(x-1)

The denominator on 2nd is 2(x-1)

If we multiplied the first by 2 and the 2nd by x we would have

a common denominator of 2x(x-1)....

 

Multiply the first fraction by 2/2... (2/2)[(x+1)/(x(x-1))] = 2(x+1)/[2x(x-1)]

 

Multiply the 2nd fraction by x/x... (x/x)[-1/(2(x-1))] = -x/[(2x)(x-1)]

 

2(x+1)/[2x(x-1)] - x/[(2x)(x-1)] = [2(x+1)-x]/[(2x)(x-1)]

 

= (2x+2-x)/[(2x)(x-1)] = (x+2)/[(2x)(x-1)]