Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 150925: X2 + 3x - 10 X2 -x-2
____________ divided by __________
x+3 X+1: X2 + 3x - 10 X2 -x-2
____________ divided by __________
x+3 X+1
Answer by jim_thompson5910(8196) About Me  (Show Source):
You can put this solution on YOUR website!
((x^2+3x-10)/(x+3))/((x^2-x-2)/(x+1)) Start with the given expression.


((x^2+3x-10)/(x+3))((x+1)/(x^2-x-2)) Multiply the first fraction (x^2+3x-10)/(x+3) by the reciprocal of the second fraction (x^2-x-2)/(x+1).


(((x+5)(x-2))/(x+3))((x+1)/(x^2-x-2)) Factor x^2+3x-10 to get (x+5)*(x-2).


(((x+5)(x-2))/(x+3))((x+1)/((x+1)(x-2))) Factor x^2-x-2 to get (x+1)*(x-2).


((x+5)(x-2)(x+1))/((x+3)(x+1)(x-2)) Combine the fractions.


((x+5)highlight((x-2))highlight((x+1)))/((x+3)highlight((x+1))highlight((x-2))) Highlight the common terms.


((x+5)cross((x-2))cross((x+1)))/((x+3)cross((x+1))cross((x-2))) Cancel out the common terms.


(x+5)/(x+3) Simplify.


So ((x^2+3x-10)/(x+3))/((x^2-x-2)/(x+1)) simplifies to (x+5)/(x+3).


In other words, ((x^2+3x-10)/(x+3))/((x^2-x-2)/(x+1))=(x+5)/(x+3) where x<>-3, x<>-1, or x<>2