How do you simplify #\frac { 2} { x } + \frac { 5} { 3}#?

2 Answers
Oct 19, 2017

#(5x+6)/(3x)#

Explanation:

In order to add fractions, we want them to have a common denominator. To do this, we will multiply the first fraction by #3/3#. This is simply another form of 1, but it will enable us to obtain a common denominator when we also multiply the second fraction by #x/x#, which again is equal to 1. Since we are multiplying by forms of 1, we are not changing the problem.

#2/x + 5/3 = 2/x (3/3) + 5/3 (x/x) = (2*3)/(x*3) + (5*x)/(3*x) = 6/(3x) + (5x)/(3x) = (5x+6)/(3x)#

Oct 19, 2017

#2/x+5/3=color(blue)((6+5x)/(3x)#

Explanation:

Simpllfy:

#2/x+5/3#

In order to add or subtract fractions, they must have the same denominator. Multiply the denominators to get the least common denominator (LCD):

LCD#=##x xx3=3x#

Multiply both fractions by a fraction form of #1#, so that each fraction has the denominator #3x#. An example is #5/5=1#. Multiiplying by fraction form of #1# makes sure that the values do not change.

#2/x xxcolor(teal)3/color(teal)3+5/3xx color(magenta)x/color(magenta)x#

Simplify.

#6/(3x)+(5x)/(3x)#

Simplify.

#(6+5x)/(3x)#