You can put this solution on YOUR website! [8/(t+5)]=[(t-3)/(t^2+7t+10)+(1/3)
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8 / (t+5) = (t-3)/(t+5)(t+2) + (1/3)
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the common denominator is (t+5)(t+2)3
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multiply both sides of = by common denominator
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(8)(3)(t+2) = 3(t-3) + (t+5)(t+2)
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24t +48 = 3t-9 + t^2+7t+10
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t^2 -14t = 47
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complete the square
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t^2 -14t +49 = 47 + 49
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(t - 7)^2 = 96
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t - 7 = + or - 9.798
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t = 7 + 9.798 = 16.798 approx 16.80
t = 7 - 9.798 = -2.798 approx -2.80
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answers are checked by substituting for t in original equation
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for t = 16.80
0.367 = 0.3679
0.37 = 0.37
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for t = -2.80
3.6364 = 3.6288
3.64 = 3.63
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our answers checks
