Hi guys, I have (3ab / a+1 + a^2 / (a+1)^3) / (3ab+1 / a - 2a+1 / a(a+1)^2)
I first combine the 3ab+1 / a - 2a+1 / a(a+1)^2) and then (3ab / a+1 + a^2 / (a+1)^3) , afterwards I divide this results following a/b / c/d =a*d / b*c rule.
But I get a funny result, and even when I facor the denominator, it still doesn't comes out.
In my textbook it says it should be a / a+1 , but the closest I've got is a+1 / a+2a.
I'd really appreciate if you caould give me directions. Thank you.
Let the numerator be
N = (3ab / a+1 + a^2 / (a+1)^3)
Give the terms in N a common denominator.
N = (3ab(a+1)^2 / (a+1)^3 + a^2 / (a+1)^3)
N = (3ab(a+1)^2 + a^2) / (a+1)^3
Let the denominator be
D = (3ab+1 / a - 2a+1 / a(a+1)^2)
Give the terms in F a common denominator.
D = ((3ab+1)(a+1)^2 / a(a+1)^2 – (2a+1) / a(a+1)^2)
D = ((3ab+1)(a+1)^2 – (2a+1)} / a(a+1)^2
Make the denominators for N and D the same, giving,
N = a(3ab(a+1)^2 + a^2) / a(a+1)^3
D = (a+1)((3ab+1)(a+1)^2 – (2a+1)} / a(a+1)^3
Working now on the expression for D,
D = (a+1){3ab(a+1)^2 + (a+1)^2 – (2a + 1)} / a(a+1)^3
D = (a+1){3ab(a+1)^2 + a^2 + 2a + 1 – 2a – 1)} / a(a+1)^3
D = (a+1){3ab(a+1)^2 + a^2)} / a(a+1)^3
Comparing N and D,
N = a(3ab(a+1)^2 + a^2) / a(a+1)^3
D = (a+1){3ab(a+1)^2 + a^2)} / a(a+1)^3
Cancelling out the common terms of the quotient, we get
N/D = a/(a+1)