Solving equation containing fraction

Question

Hi, I keep getting the wrong answer to this : x — 6⁄2-x = 3x/x-2

Answer 1

Hi Alex, with this problem there is a "trick" you can use to make it simpler. 

 

The original equation:

 

x - 6 / (2 - x) = 3x / (x - 2)

 

You need to clear the fractions in order to solve the equation. If you look at the two fractions, the denominators are almost the same with one denominator being 2 - x and the other being x - 2.

 

If we multiply the first fraction by -1, we get: + 6 / (x - 2), which gives us the same denominator as the second fraction. We have not changed anything by doing this, but we get the same denominator for both fractions.

 

Modified equation:

 

x + 6 / (x - 2) = 3x / (x - 2)

 

Multiply all terms by x - 2 to clear fractions:

 

x * (x - 2) + 6 = 3x, note the denominators cancel out.

 

Clear parenthesis:

 

x² - 2x + 6 = 3x

 

Subtract 3x from both sides:

 

x² - 5x + 6 = 0

 

Factor:

 

(x -2) * (x - 3) = 0

 

Solve for x:

 

x - 2 = 0

 

x = 2

 

x - 3 = 0

 

x = 3

 

Solution:

 

x = 2, and x = 3

 

Questions?