Question

HURRY!! explain the error in this simplification. show your work as you correct the error.

Answer 1

There is an error in the second step. Before cross multiplying the denominators, LCM of the values should be taken.

Step-by-step explanation:

Step 1; 1 - $\frac{2}{x-2}$ = $\frac{x+ 1}{x+ 2}$.

By taking an LCM of x-2 on the LHS, we get

$\frac{x-2}{x-2}$ - $\frac{2}{x-2}$ = $\frac{x+ 1}{x+ 2}$,

as both terms on the LHS have same denominator, we can add them up,

$\frac{x-2-2}{x-2}$ = $\frac{x-4}{x-2}$ = $\frac{x+ 1}{x+ 2}$.

Step 2; Now we cross multiply the denominators.

(x - 4) × (x + 2) = (x + 1) × (x - 2),

x² - 2x - 8 = x² - x - 2,

(x² - 2x - 8) - (x² - x - 2) = 0.

x² - x² - 2x + x - 8 + 2 = 0,

-x -6 = 0,

x = -6.

By simplifying the given expression, we get x = -6.