1.) Determine a rule for (f+g)(x) 2.)Evaluate (f+g)(−1)

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Guest Jan 14, 2020

geno3141 · Answer 1 · 2020-01-15T02:45:42

f(x) = 5 / (x - 2)

g(x) = 2x / (x² - 4)

f(x) + g(x) = 5 / (x - 2) + 2x / (x² - 4) = 5 / (x - 2) + 2x / [ (x - 2)(x + 2) ]

= [ 5(x + 2) ] / [ (x - 2)(x + 2) ] + 2x / [ (x - 2)(x + 2) ]

= [ 5(x + 2) + 2x ] / [ (x - 2)(x + 2) ]

= [ 5x + 10 + 2x ] / [ (x - 2)(x + 2) ]

= [7x + 10] / [ (x - 2)(x + 2) ]

(f + g)(-1) = [ 7 · -1 + 10 ] [ (-1 -2)(-1 + 2) ] = 3 / -3 = -1

1.) ​ Determine a rule for (f+g)(x) 2.)Evaluate (f+g)(−1)