How do you combine #\frac { 3v } { v + 3} + \frac { 5} { 2v - 1}# into one fraction?

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Answer 1 · 2017-03-31T18:46:56

#= (6v^2+2v+15)/(2v^2+5v-3)#

For two or more fractions to be combined, they must have the same denominator.

To make this the case, find the LCM of the denominators.
(in this case, multiply them)

#LCM (v+3),(2v-1) = (v+3)(2v-1)#

#(v+3)(2v-1)=2v^2-v+6v-3#

#=2v^2+5v-3#

Then multiply the numerators:

#(3v)/(v+3) = (3v(2v-1))/(2v^2+5v-3)#

#rArr=(6v^2-3v)/(2v^2+5v-3)#

#(5)/(2v-1) = (5(v+3))/(2v^2+5v-3)#

#rArr= (5v+15)/(2v^2+5v-3)#

Now add the two fractions together:

#(6v^2-3v)/(2v^2+5v-3)+ (5v+15)/(2v^2+5v-3)#

#= (6v^2+2v+15)/(2v^2+5v-3)#