Question

$4 + \frac{x}{y} = 1$
$4 = ( - \frac{x}{y} )$
but...
$4 + \frac{x}{y} = 1$
$4 + x = 1y$
$4 = \frac{y}{x}$
or
if we take the another case
from previous step.
$4= 1y - x$
what is the wrong thing?​

Answer 1

Step-by-step explanation:

Your 2nd and 4th steps are incorrect.

$4 + \frac{x}{y} = 1$

Transpose 1, to the left and x/y, to the right,

we have,

4 - 1 = -x/y

3 = -x/y

x = -3y

If you transpose x/y in right side, then

4 = 1 - x/y

Now, multiply by 'y' in each term of the equation

4 × y = 1 × y - (x × y)/y

4y = y - x

3y = -x

x -3y

Otherwise, take LCM.

$4 + \frac{x}{y} = 1 \\ => \frac{4}{1} + \frac{x}{y} = 1 \\ => \frac{4 \times y \: + x \times 1}{y} = 1 \\ => 4y + x = 1 \times y \\ => x = y - 4y \\ => x = - 3y$

Note : you cannot multiply y only in 1 (in RHS)

leaving 4 un-multiplied in LHS.