+74 Please solve,
x-1 x+2
----- + ----- = 1
2x-4 3x
pretty darn sure I have to find x, already tried a few times, but I think I do it wrong.
Solve for x:
(x+2)/(3 x)+(x-1)/(2 x-4)=0
Bring (x+2)/(3 x)+(x-1)/(2 x-4) together using the common denominator 6 x (x-2):
(5 x^2-3 x-8)/(6 x (x-2))=0
Multiply both sides by 6:
(5 x^2-3 x-8)/(x (x-2))=0
Multiply both sides by x (x-2):
5 x^2-3 x-8=0
The left hand side factors into a product with two terms:
(x+1) (5 x-8)=0
Split into two equations:
x+1=0 or 5 x-8=0
Subtract 1 from both sides:
x=-1 or 5 x-8=0
Add 8 to both sides:
x=-1 or 5 x=8
Divide both sides by 5:
Answer: | x=-1 or x=8/5
+33661 Hmm! I think you need to check your analysis Guest. You seem to have forgotten the 1 on the right hand side!
Thanks Alan! Sorry about that.Must have been asleep!
Solve for x:
(x+2)/(3 x)+(x-1)/(2 x-4)=1
Bring (x+2)/(3 x)+(x-1)/(2 x-4) together using the common denominator 6 x (x-2):
(5 x^2-3 x-8)/(6 x (x-2))=1
Multiply both sides by 6 x (x-2):
5 x^2-3 x-8=6 x (x-2)
Expand out terms of the right hand side:
5 x^2-3 x-8=6 x^2-12 x
Subtract 6 x^2-12 x from both sides:
-x^2+9 x-8=0
The left hand side factors into a product with three terms:
-(x-8) (x-1)=0
Multiply both sides by -1:
(x-8) (x-1)=0
Split into two equations:
x-8=0 or x-1=0
Add 8 to both sides:
x=8 or x-1=0
Multiply both sides by -1:
(x-8) (x-1)=0
Split into two equations:
x-8=0 or x-1=0
Add 8 to both sides:
x=8 or x-1=0
Add 1 to both sides:
Answer: | x=8 or x=1
