Question

Fill in the missing term in the equation. x/x^2-4x+4-x/x^2-3x+2=?/(x-2)^2(x-1)

Answer 1

Answer:

The missing term is x.

Step-by-step explanation:

Given expression is,

$\frac{x}{x^2-4x+4}-\frac{x}{x^2-3x+2}------(1)$

Since, $x^2-4x+4=(x)^2-2\times (2x)+(2)^2$

$\implies x^2-4x+4=(x-2)^2------(2)$    ( (a-b)² = a² - 2ab + b² )

Now,   $x^2-3x+2=x^2-2x-x+2$    ( By middle term splitting )

$=x(x-2)-1(x-2)$

$\implies x^2-3x+2=(x-1)(x-2)------(3)$

From equation (1), (2) and (3),

$\frac{x}{x^2-4x+4}-\frac{x}{x^2-3x+2}=\frac{x}{(x-2)^2}-\frac{x}{(x-2)(x-1)}$

$=\frac{x(x-1)-x(x-2)}{(x-2)^2(x-1)}$

$=\frac{x(x-1-x+2)}{(x-2)^2(x-1)}$

$=\frac{x(1)}{(x-2)^2(x-1)}$

$=\frac{x}{(x-2)^2(x-1)}$

Hence, the missing term in the equation is x.

Answer 2

           x                            x
-----------------  -  --------------------
x^2 -4x + 4            x^2-3x+2

           x                            x
= ----------------  -  --------------------
    (x -2)^2            (x - 2)(x - 1)

        x (x-1)  - x(x +2)                       
= ----------------------------
          (x -2)^2 (x - 1)

      x^2 -x -x^2 - 2x                    
= --------------------------
      (x -2)^2 (x - 1)

           -3x                    
= -----------------------
      (x -2)^2 (x - 1)

answer 
missing term in the equation: -3x