How can you evaluate #(k-4h+2)/(2k)+(4k+3h-1)/(7k)#?

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Answer 1 · 2015-08-14T19:08:53

#(15k - 22h + 12)/(14k)#

Notice that you need to add two fractions, one that has the denominator equal to #2k#, and the other one that has the denominator equal to #7k#.

Right from the start, the first thing that you need to do is find the common denominator, which in your case is #14k#.

To get both fractions to have the same denominator, multiply the first one by #7/7# and the second one by #2/2#. This will get you

#(7 * (k - 4h + 2))/(7 * 2k) + (2 * (4k + 3h - 1))/(2 * 7k)#

#(7k - 28h + 14)/(14k) + (8k + 6h - 2)/(14k)#

Now simply add the two numerators to get

#(7k - 28h + 14 + 8k + 6h - 2)/(14k)#

To simplify this fraction, combine like terms

#(7k + 8k - 28h + 6h + 14 - 2)/(14k)#

#color(green)((15k - 22h + 12)/(14k))#