solve for x ---> x/(x-2) = 2/(x-3)?

Question

answer is 1 or 4

Answer 1

Multiply both sides by (x-2)(x-3): x(x-3)=2(x-2)

x^2-3x=2x-4
x^2-5x+4=0
(x-1)(x-4)=0
x=1 or 4

Answer 2

Yes its 1 and 4,
x(x-3)=2(x-2),
x^2-5x+4=0,
( x-4)(x-1)
x=4 and x=1

Answer 3

x/(x-2) = 2/(x-3) Cross multiplying we get
x(x-3) = 2(x-2)

x² - 3x = 2x -4 Taking 2x - 4 to the other side , the sign changes ( + to - and - to +)
x²-3x-2x+4 = 0
x²-5x+4 = 0
x² -x -4x + 4 = 0
x(x-1) -4(x-1) = 0
(x-1) (x-4) = 0
x-1 = 0 therefore x = 1
x-4 = 0 therefore x = 4

therefore x = 1 or 4

Answer 4

do cross-products and get
x(x-3) = 2(x-2)
x² - 3x = 2x - 4
x² - 5x + 4 = 0
(x - 1)(x - 4) = 0
when each factor is set= to 0 and solved
you get x=1 or x=4
~~

Answer 5

x/(x-2) = 2/(x-3)
x(x-3)=2(x-2)
x^2-3x=2x-4
x^2-5x+4=0
(x-4)(x-1)=0
x = 4 or 1

Answer 6

first, we do cross multiplication
x(x-3)=2(x-2)

then multiply
(x^2-3x)=(2x-4)

add 3x to both sides to cancel (-3x)
x^2=5x-4

add (-5x) to both sides to cancel 5x
x^2-5x=(-4)

add 4 to both sides to cancel (-4)
x^2-5x+4=0

factor the trinomial
(x-4)(x-1)=0

find what values will make the equation true
solution set: {x/x=4 or x=1}

hope i helped! ^_^v

Answer 7

x / (x-2) =2/ (x-3)

lcd is x-2 x-3

x(x-3)=2(x-2)
-------------------
x^2-5x+6

x^2-3x=2x-4

x^2-5x+4=0


(x-1)(x-4) answer is 1 or 4 is correct

Answer 8

x(x-3)/(x-2)(x-3) = 2(x-2)/(x-3)(x-2)
x²-3x=2x-4
x²-3x-2x+4=0
x²-5x+4=0
(x-1)(x-4)