SOLUTION: Hello, the question asks to simplify the following algebraic expression. I apologize if this isn't the correct topic I have selected. The question is: "Simplify the following algeb

Algebra ->  Expressions -> SOLUTION: Hello, the question asks to simplify the following algebraic expression. I apologize if this isn't the correct topic I have selected. The question is: "Simplify the following algeb      Log On


   

Question 977750: Hello, the question asks to simplify the following algebraic expression. I apologize if this isn't the correct topic I have selected. The question is: "Simplify the following algebraic expression:((x+1)^3 (3x-5) - (x+1)^2 (8x+3))/(x-4)(x+1)^3
Found 3 solutions by Alan3354, Fombitz, Boreal:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%2B1%29%5E3+%283x-5%29+-+%28x%2B1%29%5E2+%288x%2B3%29%29%2F%28x-4%29%28x%2B1%29%5E3
Cancel (x+1)^2
= %28%28x%2B1%29+%283x-5%29+-+%288x%2B3%29%29%2F%28x-4%29%28x%2B1%29
= %28%283x%5E2+-+2x+-+5%29+-+%288x%2B3%29%29%2F%28x-4%29%28x%2B1%29
= %283x%5E2+-+10x+-+8%29%2F%28x-4%29%28x%2B1%29
= %28%283x%2B2%29%2A%28x+-4%29%29%2F%28x-4%29%28x%2B1%29
= %283x%2B2%29%2F%28x%2B1%29

Answer by Fombitz(32388) About Me  (Show Source):
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
((x+1)^3 (3x-5) - (x+1)^2 (8x+3))/(x-4)(x+1)^3=
((x+1)^3)(3x-5))/(x-4) (x+1)^3 minus (x+1)^2(8x+3)/(x-4) (x+1)^3. Split the fraction.

Cancel the (x+1)^3 completely in the first numerator term and (x+1)^2 in the second term.
This leaves
[(3x-5)/(x-4)] - ((8x+3)/(x+1)

common denominator is (x-4)(x+1)
numerator will be (3x-5)(x+1)=3x^2-17x20 - [8x+3)(x-4)]
second part is 8x^2-29x-12,
3x^2-17x+20-8x^2+29x+12= {-5x^2+12x+32}/(x-4)(x+1)= -(5x^2-12x-32)/(x-4)(x+1)=
-(5x+8)(x-4)/(x-4)(x+1)= -(5x+8)/(x+1), because the (x-4) divide out.
Notice that I pull a minus sign out of the equation, because factoring -x^2 terms is difficult.
Do not multiply out the numerator at first. Split it into two fractions, cancel what you can, then put everything over a common denominator and simplify that. Often you can cancel further.