SOLUTION: Suppose 1/(2x � 4) + 1/(x � 2) = 3/2. What is x? This is a question from my teacher. I think I'm supposed to add the first two equations, then cross multiply that answer by 3/2 to

Question 133463: Suppose 1/(2x � 4) + 1/(x � 2) = 3/2. What is x?
This is a question from my teacher. I think I'm supposed to add the first two equations, then cross multiply that answer by 3/2 to get the answer, but I'ts just not coming together for me.
Found 3 solutions by vleith, checkley71, josmiceli:
Answer by vleith(2983)   (Show Source): You can put this solution on YOUR website!
First thing to do is to find a common denominator
1/(2x � 4) + 1/(x � 2) = 3/2

Now you cross multiply.

Now collect like terms

Divide through by 6

Finally factor and solve

x = 6, x = -1
Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
1/(2X-4)+1/(X-2)=3/2 COMBINE THE 2 FRACTIONS BY FINDING A COMMON DENOMINATOR WHICH IS (2X-4)(X-2).
(X-2+2X-4)/(2X-4)(X-2)=3/2
(3X-6)/(2X^2-8X+8)=3/2 NOW CROSS MULTIPLY
3(2X^2-8X+8)=2(3X-6)
6X^2-24X+24=6X-12
6X^2-24X-6X+24+12=0
6X^2-30X+36=0
6(X^2-5X+6)=0
6(X-3)(X-2)=0
X-3=0
X=3 ANSWER.
X-2=0
X=2 ANSWER.

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

multiply both sides by

Divide both sides by

check:

Multiply both sides by

OK
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