How do you evaluate #3x ( x + 2) ^ { - \frac { 1} { 3} } + 4( x + 2) ^ { \frac { 2} { 3} }#?

2 Answers
Jim G.
Feb 11, 2018

#(7x+8)/(x+2)^(1/3)#

Explanation:

#"to factorise and simplify"#

#"take out a "color(blue)"common factor of "(x+2)^(-1/3)#

#=(x+2)^(-1/3)[3x+4(x+2)]#

#=(x+2)^(-1/3)(7x+8)=(7x+8)/(x+2)^(1/3)#

Shwetank Mauria
Feb 11, 2018

#3x(x+2)^(-1/3)+4(x+2)^(2/3)=(7x+2)(x+2)^(-1/3)#

Explanation:

#3x(x+2)^(-1/3)+4(x+2)^(2/3)#

= #3x(x+2)^(-1/3)+4(x+2)^(1-1/3)#

= #3x(x+2)^(-1/3)+4(x+2)^1xx(x+2)^(-1/3)#

= #(x+2)^(-1/3)[3x+4(x+2)]#

= #(7x+2)(x+2)^(-1/3)#

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