SOLUTION: {{{(a(x+1)+b(x-1))/(x-2)=2+(1/(x-2))}}}
The equation above is true for all values of x≠2, where a and b are constats. What is the value of a?
A) -1/2
B) 2
C) 3
D) 4
Algebra.Com
Question 1043622:
The equation above is true for all values of x≠2, where a and b are constats. What is the value of a?
A) -1/2
B) 2
C) 3
D) 4
Found 2 solutions by jim_thompson5910, rothauserc:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
For now, I'm going to simplify the right side only
Now I'm going to rearrange terms on the left side
Take note that the x term on the left side numerator is . The x term on the right side numerator is . Equate the coefficients to get this equation
The constant terms on the left side numerator is . The constant terms on the right side numerator is . Equate the terms to get the equation
--------------------------------------------------------------
We have this system of equations
Let's add the two equations up
a+b=2
a-b=-3
-------
2a+0b=-1
So . Divide both sides by 2 to isolate 'a'. Doing this will lead to
So the answer is choice A) -1/2
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
2 + ( 1 / (x-2) ) = (2x-3) / (x-2), then
:
a(x+1) + b(x-1) = 2x-3
:
ax+a +bx-b = 2x-3
:
we have two equations in 2 unknowns
:
1) ax +bx = 2x
2) a -b = -3
:
solve 2) for b
:
b = a +3
:
substitute for b in equation 1)
:
ax +(a+3)x = 2x
:
2ax = -x
:
************
a = -0.5
answer is A)
************
:
check our answer
a = -0.5, then b = -0.5 +3 = 2.5
:
substitute for a and b in the original equation
:
(-0.5(x+1) + 2.5(x-1)) / (x-2) =
:
(-0.5x -0.5 +2.5x -2.5) / (x-2) =
:
(2x - 3) / (x-2) = 2 + ( 1 / (x-2) ) = (2x -3) / (x-2)
:
our answer checks :-)
:
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