How do you combine like terms in #\frac { 11z - 7} { 3z } + \frac { 4z + 1} { 3z }#?

1 Answer
smendyka
Apr 17, 2017

See the entire solution process below:

Explanation:

Because both fractions have a common denominator we can add the numerators over the common denominator:

#((11z - 7) + (4z + 1))/(3z) = (11z - 7 + 4z + 1)/(3z)#

Next, group like terms in the numerator:

#(11z + 4z - 7 + 1)/(3z)#

Now, combine like terms in the numerator:

#((11 + 4)z + (-7 + 1))/(3z)#

#(15z + (-6))/(3z)#

#(15z - 6)/(3z)# Where #z != 0#

We can also, if required, separate this as:

#(15z)/(3z) - 6/(3z) = (color(red)(cancel(color(black)(15)))5color(blue)(cancel(color(black)(z))))/(color(red)(cancel(color(black)(3)))color(blue)(cancel(color(black)(z)))) - (color(red)(cancel(color(black)(6)))2)/(color(red)(cancel(color(black)(3)))z) =#

#5 - 2/z# Where #z != 0#

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