Rearrange the formula y = 3x-2/x+1 to make x the subject.

I found this in a test paper, and am struggling to finish it. I have gotten to yx+y=3x-2 but don't know where to go from there.

Guest Jan 16, 2016

#1**+10 **

Solve for x:

y = 3 x+1-2/x

y = 3 x+1-2/x is equivalent to 3 x+1-2/x = y:

3 x+1-2/x = y

Bring 3 x+1-2/x together using the common denominator x:

(3 x^2+x-2)/x = y

Multiply both sides by x:

3 x^2+x-2 = x y

Subtract x y from both sides:

-2+x+3 x^2-x y = 0

Collect in terms of x:

-2+3 x^2+x (1-y) = 0

Divide both sides by 3:

-2/3+x^2+1/3 x (1-y) = 0

Add 2/3 to both sides:

x^2+1/3 x (1-y) = 2/3

Add 1/36 (1-y)^2 to both sides:

x^2+1/3 x (1-y)+1/36 (1-y)^2 = 2/3+1/36 (1-y)^2

Write the left hand side as a square:

(x+(1-y)/6)^2 = 2/3+1/36 (1-y)^2

Take the square root of both sides:

x+(1-y)/6 = sqrt(2/3+1/36 (1-y)^2) or x+(1-y)/6 = -sqrt(2/3+1/36 (1-y)^2)

Subtract (1-y)/6 from both sides:

x = sqrt(2/3+1/36 (1-y)^2)+(y-1)/6 or x+(1-y)/6 = -sqrt(2/3+1/36 (1-y)^2)

Subtract (1-y)/6 from both sides:

**Answer: | x = sqrt(2/3+1/36 (1-y)^2)+(y-1)/6 or x = (y-1)/6-sqrt(2/3+1/36 (1-y)^2)**

Guest Jan 16, 2016

#1**+10 **

Best Answer

Solve for x:

y = 3 x+1-2/x

y = 3 x+1-2/x is equivalent to 3 x+1-2/x = y:

3 x+1-2/x = y

Bring 3 x+1-2/x together using the common denominator x:

(3 x^2+x-2)/x = y

Multiply both sides by x:

3 x^2+x-2 = x y

Subtract x y from both sides:

-2+x+3 x^2-x y = 0

Collect in terms of x:

-2+3 x^2+x (1-y) = 0

Divide both sides by 3:

-2/3+x^2+1/3 x (1-y) = 0

Add 2/3 to both sides:

x^2+1/3 x (1-y) = 2/3

Add 1/36 (1-y)^2 to both sides:

x^2+1/3 x (1-y)+1/36 (1-y)^2 = 2/3+1/36 (1-y)^2

Write the left hand side as a square:

(x+(1-y)/6)^2 = 2/3+1/36 (1-y)^2

Take the square root of both sides:

x+(1-y)/6 = sqrt(2/3+1/36 (1-y)^2) or x+(1-y)/6 = -sqrt(2/3+1/36 (1-y)^2)

Subtract (1-y)/6 from both sides:

x = sqrt(2/3+1/36 (1-y)^2)+(y-1)/6 or x+(1-y)/6 = -sqrt(2/3+1/36 (1-y)^2)

Subtract (1-y)/6 from both sides:

**Answer: | x = sqrt(2/3+1/36 (1-y)^2)+(y-1)/6 or x = (y-1)/6-sqrt(2/3+1/36 (1-y)^2)**

Guest Jan 16, 2016

#2**+5 **

....the question wasn't to solve it, it was to rearrange it to make x the subject

Guest Jan 16, 2016