Answer:
[tex]\dfrac{-1}{7(x-2)}+\dfrac{15}{7(x+5)}[/tex]
Step-by-step explanation:
For f(x) = (2x-5)/((x -2)(x +5)), the decomposition will be of the form ...
f(x) = A/(x -2) +B/(x +5)
The values of A and B can be found from ...
A = (x -2)f(x) evaluated at x=2
A = (2·2-5)/(2+5) = -1/7
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B = (x +5)f(x) evaluated at x=-5
B = (2(-5) -5)/(-5-2) = -15/-7 = 15/7
[tex]\dfrac{2x-5}{x^2+3x-10}=\bf{\dfrac{-1}{7(x-2)}+\dfrac{15}{7(x+5)}}[/tex]
