The rational function that has the same graph as f(x) = 2x²+3x-5 / x³-2x²+5x-1 is: B) f(x) = 2x+3 / x²-2x+5
To determine this, we first need to factor both numerators and denominators of the two given functions.
For f(x) = 2x²+3x-5 / x³-2x²+5x-1:
Numerator: 2x²+3x-5 can be factored as (x-1)(2x+5)
Denominator: x³-2x²+5x-1 can be factored as (x-1)(x²-x+5)
For f(x) = 2x+3 / x²-2x+5:
Numerator: 2x+3 cannot be factored further
Denominator: x²-2x+5 cannot be factored further
Now, if we divide the numerator and denominator of the first function by (x-1), we get:
f(x) = (2x+5) / (x²-x+5)
This is the simplified form of f(x) = 2x²+3x-5 / x³-2x²+5x-1.
Complete question:
What is the rational function
A) f(×)= 2ײ+3×-5
׳-2ײ+5×1