Answer:
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
__
B = (x +5)f(x) evaluated at x=-5
B = (2(-5) -5)/(-5-2) = -15/-7 = 15/7
Answer:
Step-by-step explanation:
Please use parentheses around the denominator:
2x
f(x) = -------------- or f(x) = 2x / (1-x^2)
1 - x^2
to eliminate any ambiguity. The graph of this function passes thru the origin (0,0) and has vertical asymptotes at x = -1 and x = + 1. The function is negative on (-1,0) and positive on (0,1).
Additionally, there are two horizontal asymptotes. As x grows large and negative, f(x) approaches zero from above. As x grows large and positive, f(x) approaches zero from below.
1/4 = 25/100
25/100 > 15/100
hope this helps