How do you combine like terms in #-\frac { 43} { 5} n + \frac { 40} { 7} + \frac { 7} { 2} n - \frac { 17} { 10}#?

1 Answer
smendyka
Jul 2, 2017

See a solution process below:

Explanation:

First, group the like terms together:

#(-43/5n + 7/2n) + (40/7 - 17/10)#

Next, we can factor the #n# out of the term on the left:

#(-43/5 + 7/2)n + (40/7 - 17/10)#

Then, we need to get each set of fractions over common denominators to be able to add or subtract them. We need to multiply each fraction by the appropriate form of #1# to accomplish this:

#((2/2 xx -43/5) + (5/5 xx 7/2))n + ((10/10 xx 40/7) - (7/7 xx 17/10))#

#(-86/10 + 35/10)n + (400/70 - 119/70)#

Now, add the fractions:

#(-86 + 35)/10n + (400 - 119)/70#

#-51/10n + 281/70#

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