How do you add #\frac { 1} { x + 1} + \frac { 2} { x - 1}#?

1 Answer
Jim G.
Feb 18, 2017

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

Explanation:

Before we can add 2 fractions we require them to have a #color(blue)"common denominator"#

To achieve this multiply the numerator/denominator of each fraction by the denominator of the other fraction.

#rArr1/color(blue)(x+1)+2/color(red)(x-1)#

#=1/color(blue)(x+1)xxcolor(red)(x-1)/color(red)(x-1)+2/color(red)(x-1)xxcolor(blue)(x+1)/color(blue)(x+1)#

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

Now the fractions have a common denominator we can add the numerators while leaving the common denominator.

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

#=(3x+1)/((x+1)(x-1))#

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