SOLUTION:
-1 + ((x - b)( x - c ))/((a-b)(a-c)) +( (x - a)(x - b))/((c-a)(c-b)) +( (x - a)(x - c))/((b-a)(b-c))
I hope this makes sense from how I typed it. It needs to be simplified
Algebra ->
Expressions-with-variables
-> SOLUTION:
-1 + ((x - b)( x - c ))/((a-b)(a-c)) +( (x - a)(x - b))/((c-a)(c-b)) +( (x - a)(x - c))/((b-a)(b-c))
I hope this makes sense from how I typed it. It needs to be simplified
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Question 753443:
-1 + ((x - b)( x - c ))/((a-b)(a-c)) +( (x - a)(x - b))/((c-a)(c-b)) +( (x - a)(x - c))/((b-a)(b-c))
I hope this makes sense from how I typed it. It needs to be simplified. I would really appreciate your help and direction.
You can put this solution on YOUR website! The simplification is relatively lengthy so I will outline it:
First off we set aside the -1 term and simplify the rational expression part.
the lcd is
(a-b)(a-c)(b-c)
After some labor we arrive at these results:
x^2 terms: 0
ax terms: abx-acx
bx terms: bcx-abx
cx terms: acx-bcx
bc terms: bc(b-c)
ab terms: ab(a-b)
ac terms: -ac(a-c)
After collecting like terms we find that all x-terms add out (cancel each other to get a sum of 0)
Leaving us with
ab(a-b)-ac(a-c)+bc(b-c)
which is equal to (a-b)(a-c)(b-c), the denominator!
Therefore our rational expression simplifies to 1 so that the entire expression evaluates to 0
