Given y=3x/(x^2-9) determine the numbers m and n if y=m/(x-3)+n/(x+3)

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We are given that y = 3x / (x^2 - 9). We have to determine m and n if y = m/(x - 3) + n/(x +3)

Equate the two expressions for y.

3x / (x^2 - 9) = m/(x - 3) + n/(x +3)

=> 3x / (x^2 - 9) = [m(x + 3) + n(x- 3)] / (x- 3)(x+3)

=> 3x / (x^2 - 9) = [mx + 3m + nx- 3n] / (x^2 - 9)

=> 3x = mx + 3m + nx- 3n

equate the coefficients of x and the numeric term

=> 3 = m + n and 3m - 3n = 0

3m - 3n = 0

=> m = n

subtitute in 3 = m + n

=> 3 = 2m

=> m = 3/2

And n = 3/2

Therefore m = 3/2 and n = 3/2.

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