How do you evaluate #x( x + 1) ( \frac { 1} { x + 1} - \frac { 4} { x } )#?

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Answer 1 · 2018-02-11T08:30:00

The expression simplifies to #- 3x -4#

Evaluate
#color(blue)(x(x+1)##((1)/(x+1)−(4)/(x))#

Solve the subtraction of fractions problem inside the parentheses

#1)# Convert the terms inside the parentheses to a fraction with the common denominator of #x(x+1)#

#color(blue)(((x(x+1))/(1))# #((1x-4(x + 1))/(x(x+1)))#

#2)# Cancel #x(x+1)# from the top and the bottom
#1x - 4(x+1)#

#3)# Clear the parentheses by distributing the #-4#
#1x - 4x - 4#

#4)# Combine like terms
#- 3x - 4# #larr# answer

#"Answer:"#
#- 3x -4#