Substitute 
, so that
Then the resulting ODE in 
is separable, with
On the left, we can split into partial fractions:
Integrating both sides gives
Now solve for 
:
Answer:
$3750
Step-by-step explanation:
Amount = principal + interest
Simple interest = Principal *Rate * time/100
Simple interest = 2500*10*5/100
Simple interest = 25*50
Simple interest = $1250
Amount = $2500+$1250
Amount after 5 years is $3750
F(x)=2x^2-x-6
Factoring:
f(x)=2(2x^2-x-6)/2=(2^2x^2-2x-12)/2=[(2x)^2-(2x)-12]/2
f(x)=(2x-4)(2x+3)/2=(2x/2-4/2)(2x+3)→f(x)=(x-2)(2x+3)
g(x)=x^2-4
Factoring
g(x)=[sqrt(x^2)-sqrt(4)][sqrt(x^2)+sqrt(4)]
g(x)=(x-2)(x+2)
f(x)/g(x)=[(x-2)(2x+3)] / [(x-2)(x+2)
Simplifying:
f(x)/g(x)=(2x+3)/(x+2)
Answer: Third Option (2x+3)/(x+2)
