Indicated sums and differences?

Question

Find the Indicated sums and differences.

1.(x-y OVER x+y) - (y-x OVER x+y)

2. (2k OVER 4k^2-9) + (3 OVER 4k^2-9)


thanks to anybody that can help!

Answer 1

1.

(x - y)/(x + y) - (y - x)/(x + y)

(x - y)/(x + y) + (x - y)/(x + y)

2(x - y)/(x + y)

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2.

2k/(4k²-9) + 3/(4k²-9)

(2k + 3)/(4k²-9)

but 4k² - 9 = (2k - 3)(2k + 3) so

(2k + 3)/(4k²-9) = (2k + 3)/[(2k - 3)(2k + 3)] = 1/(2k-3)

since 4k² - 9 = 0 would make the equation undefined, k≠±1½

Answer 2

Question 1
(x - y) / (x + y) - (y - x) / (x + y)
(x - y) / (x + y) + (x - y) / (x + y)
= 2.(x - y) / (x + y)

Question 2
= 2k / (2k - 7).(2k + 7) + 3 / (2k - 7).(2k + 7)
= (2k + 3) / [(2k - 7).(2k + 7) ]

Answer 3

In both cases you have common denominators. Just add the numerators.