How do you add #\frac { 4x - 2} { 5x + 10} + \frac { x + 4} { x + 2}#?

1 Answer
Aug 2, 2017

sum is #9/5#

Explanation:

This is another way to solve the problem.

When you add fractions, you need to have the same denominator for all. In this case, you have two denominators, 5x+10 and x+2. Since these are different, you want to find a common denominator between the two. If you notice, if you multiple x+2 by 5, you get 5x+10. So, 5x+10 is the denominator for the answer.

Now, we have to change the second fraction. Remember, when you change the denominator, you have to change the numerator. In this case, we are multiplying the top and bottom by 5.

#(5(x+4))/(5(x+2))# = #(5x+20)/(5x+10)#.

Now we can add the two fractions together.

#(4x-2)/(5x+10)+(5x+20)/(5x+10)# = #(4x-2+5x+20)/(5x+10)# = #(9x+18)/(5x+10)#

Finally, you simplify the equation. In this case, the numerator and denominator have a common factor of x+2. When we simplify, the answer becomes #9/5#.

#(9x+18)/(5x+10)# = #(9(x+2))/(5(x+2))# = #9/5#